Preprints 2022

Boundaries in Free Higher Derivative Conformal Field Theories
Authors: Adam Chalabi, Christopher P. Herzog, Krishnendu Ray, Brandon Robinson, Jacopo Sisti, Andreas Stergiou
Preprint number: UUITP53/22
We consider free higher derivative theories of scalars and Dirac fermions in the
presence of a boundary in general dimension. We establish a method for finding consistent
conformal boundary conditions in these theories by removing certain boundary primaries
from the spectrum. A rich set of renormalization group flows between various conformal
boundary conditions is revealed, triggered by deformations quadratic in the boundary pri
maries. We compute the free energy of these theories on a hemisphere, and show that the
boundary atheorem is generally violated along boundary flows as a consequence of bulk
nonunitarity. We further characterize the boundary theory by computing the twopoint
function of the displacement operator. 
A comment on Metric vs MetricAffine Gravity
Authors: Ulf Lindström and Özgür Sarıoğlu
Preprint number: UUITP52/22
We consider the sum of the EinsteinHilbert action and a Pontryagin density (PD) in arbitrary{even} dimension $D$. All curvatures are functions of independent affine (torsionless) connections only. In arbitrary dimension, not only in $D=4n$, these first order PD terms are shown to be covariant divergences of ``ChernSimons'' currents. The field equation for the connection leads to it being LeviCivita, and to the metric and affine field equations being equivalent to the second order metric theory. This result is a counterexample to the theorem stating that purely metric and metricaffine models can only be equivalent for Lovelock theories. 
Cyclic products of Szegö kernels and spin structure sums
Authors: Eric D'Hoker, Martijn Hidding and Oliver Schlotterer
Preprint number: UUITP51/22
The summation over spin structures, which is required to implement the GSO projection in the RNS formulation of superstring theories, often presents a significant impediment to the explicit evaluation of superstring amplitudes. In this paper we discover that, for Riemann surfaces of genus two and even spin structures, a collection of novel identities leads to a dramatic simplification of the spin structure sum. Explicit formulas for an arbitrary number of vertex points are obtained in two steps. First, we show that the spin structure dependence of a cyclic product of Szegö kernels (i.e. Dirac propagators for worldsheet fermions) may be reduced to the spin structure dependence of the fourpoint function. Of particular importance are certain trilinear relations that we shall define and prove. In a second step, the known expressions for the genustwo even spin structure measure are used to perform the remaining spin structure sums. The dependence of the spin summand on the vertex points is reduced to simple building blocks that can already be identified from the twopoint function. The hyperelliptic formulation of genustwo Riemann surfaces is used to derive these results, and its SL(2,C) covariance is employed to organize the calculations and the structure of the final formulas. The translation of these results into the language of Riemann thetafunctions, and applications to the evaluation of higherpoint string amplitudes, are relegated to subsequent companion papers.

Noninvertible Symmetries of Class S Theories
Authors: Vladimir Bashmakov, Azeem Hasan, Michele Del Zotto, Justin Kaidi
Preprint number: UUITP50/22
Abstract: We study the noninvertible symmetries of class S theories obtained by compactifying the type $a_{p−1}$ 6d (2,0) theory on a genus g Riemann surface with no punctures. After setting up the general framework, we describe how such symmetries can be classified up to genus 5. Of central interest to us is the question of whether a noninvertible symmetry is intrinsic, i.e. whether it can be related to an invertible symmetry by discrete gauging. We then describe the higherdimensional origin of our results, and explain how the Anomaly and Symmetry TFTs, as well as Nality defects, of class S theories can be obtained from compactification of a 7d ChernSimons theory. Interestingly, we find that the Symmetry TFT for theories with intrinsically noninvertible symmetries can only be obtained by coupling the 7d ChernSimons theory to topological gravity.

A stringy realization of dark bubble cosmology
Authors: Ulf Danielsson, Oscar Henriksson, Daniel Panizo
Preprint number: UUITP49/22
Abstract: In this paper we construct a stringy embedding of the dark bubble model of an expanding 4D cosmology. The universe rides a bubble of true vacuum, which has nucleated in an unstable higher dimensional background. Our construction is a string theoretical realization of Vilenkin’s quantum cosmology. Even though the cosmological constant vanishes at lowest order, higher order corrections, implementing the WGC, induce a phenomenologically viable cosmological constant. We discuss a possible connection with the dark dimension.

From the EFT of Spinning Gravitating Objects to Poincaré and Gauge Invariance
Authors: Michèle Levi, Roger Morales, Zhewei Yin
Preprint number: UUITP48/22
In this paper we confirm the generalized actions of the complete NLO cubicinspin interactions for generic compact objects which were tackled first via an extension of the EFT of spinning gravitating objects. The interaction potentials are made up of 6 independent sectors, including a new unique sector that is proportional to the square of the quadrupolar deformation parameter, C_{ES^2}. We derived the full Hamiltonians in an arbitrary reference frame and in generic kinematic configurations. Using these most general Hamiltonians we find the full Poincaré algebra of all the sectors at the 4.5PN order, including the third subleading spinorbit sector recently derived within our approach. We also derive the binding energies with gaugeinvariant relations useful for gravitationalwave applications. Finally, we derive the extrapolated scattering angles in the alignedspins case, and we find complete agreement with previous results derived for the scattering of black holes via scatteringamplitudes methods. The completion of the full Poincaré algebra at the 4.5PN order provides a strong validation that this new precision frontier in PN theory has now been established.

Colorkinematics dual representations of oneloop matrix elements in the opensuperstring effective action
Authors: Alex Edison and Micah Tegevi
Preprint number: UUITP47/22
The alpha'expansion of string theory provides a rich set of higherdimension operators, indexed by zeta values, which can be used to study colorkinematics duality and the double copy. These two powerful properties, actually first noticed in treelevel string amplitudes, simplify the construction of both gauge and gravity amplitudes. However, their applicability and limitations are not fully understood. We attempt to construct a set of colorkinematics dual numerators at one loop and four points for insertions of operator combinations corresponding to the lowest four zeta_2free operator insertions from the open superstring: zeta_3, zeta_5, zeta_3^2, and zeta_7. We succeed in finding a representation for the first three in terms of box, triangle, and bubble numerators. In the case of zeta_7 we find an obstruction to a fully colordual representation related to the regularization of bubbleonexternalleg type diagrams. The simplest regularization approach leads to an overconstrained system, signaling an incompatibility between the chosen regularization and colorkinematics duality. Using the constructed colordual numerators, we find two different BernCarrascoJohansson double copies that produce candidate closedstringinsertion numerators. Both approaches to the double copy match the kinematics of the cuts, with relative normalization set by either summing over both double copies including degeneracy or by including an explicit prefactor on the doublecopy numerator definitions.

Angular Momentum Loss Due to Tidal Effects in the PostMinkowskian Expansion
Author: Carlo Heissenberg
Preprint number: UUITP46/22
We calculate the tidal corrections to the loss of angular momentum in a twobody collision at leading PostMinkowskian order from an amplitudebased approach. The eikonal operator allows us to efficiently combine elastic and inelastic amplitudes, and captures both the contributions due to genuine gravitationalwave emissions and those due to the static gravitational field. We calculate the former by harnessing powerful colliderphysics techniques such as reverseunitarity, thereby reducing them to cut twoloop integrals, and validate the result with an independent calculation in the PostNewtonian limit. For the latter, we can employ the results of arXiv:2203.11915 where staticfield effects were calculated for generic gravitational scattering events using the leading soft graviton theorem.

Perfecting oneloop BCJ numerators in SYM and supergravity
Authors: Alex Edison, Song He, Henrik Johansson, Oliver Schlotterer, Fei Teng, Yong Zhang
Preprint number: UUITP45/22
We take a major step towards computing Ddimensional oneloop amplitudes in general gauge theories, compatible with the principles of unitarity and the colorkinematics duality. For npoint amplitudes with either supersymmetry multiplets or generic nonsupersymmetric matter in the loop, simple allmultiplicity expressions are obtained for the maximal cuts of kinematic numerators of ngon diagrams. At n=6,7 points with maximal supersymmetry, we extend the cubicdiagram numerators to encode all contact terms, and thus solve the longstanding problem of \emph{simultaneously} realizing the following properties: colorkinematics duality, manifest locality, optimal power counting of loop momenta, quadratic rather than linearized Feynman propagators, compatibility with double copy as well as all graph symmetries. Colorkinematics dual representations with similar properties are presented in the halfmaximally supersymmetric case at n=4,5 points. The resulting gaugetheory integrands and their supergravity counterparts obtained from the double copy are checked to reproduce the expected ultraviolet divergences.

Treelevel amplitudes from the pure spinor superstring
Authors: Carlos R. Mafra and Oliver Schlotterer
Preprint number: UUITP44/22
We give a comprehensive review of recent developments on using the pure spinor formalism to compute massless superstring scattering amplitudes at tree level. The main results of the pure spinor computations are placed into the context of related topics including the colorkinematics duality in field theory and the mathematical structure of alpha'corrections.

Gravitational duality, Palatini variation and boundary terms: A synopsis.
Authors: Ulf Lindström and Özgur Sarioglu
Preprint number: UUITP43/22
We consider $f(R)$ gravity and BornInfeldEinstein (BIE) gravity in formulations where the metric and connection are treated independently and integrate out the metric to find the corresponding models solely in terms of the connection, the archetypical treatment being that of EddingtonSchr\"odinger (ES) duality between cosmological Einstein and Eddington theories. For dimensions $D\ne2$, we find that this requires $f(R)$ to have a specific form which makes the model Weyl invariant, and that its Eddington reduction is then equivalent to that of BIE with certain parameters. For $D=2$ dimensions, where ES duality is not applicable, we find that both models are Weyl invariant and equivalent to a first order formulation of the bosonic string. We also discuss the form of the boundary terms needed for the variational principle to be well defined on manifolds with boundaries.This requires a modification of the GibbonsHawkingYork boundary term for gravity. This modification also means that the dualities between metric and connection formulations include the boundary terms. 
Classical Gravitational Observables from the Eikonal Operator
Authors: Paolo Di Vecchia, Carlo Heissenberg, Rodolfo Russo, Gabriele Veneziano
Preprint number: UUITP42/22
We propose two possible eikonal operators encoding the effects of
classical radiation as coherent states of gravitons and show how to
compute from them different classical observables. In the first proposal,
only genuinely propagating gravitons are included, while, in the second,
zerofrequency modes are added in order to recover the effects of a static
gravitational field. We first calculate the radiated energymomentum and
the change in each particle's momentum, or impulse, to 3PM order finding
agreement with the literature. We then calculate the angular momentum of
the gravitational field after the collision. In order to do so, we adapt
the method of reverse unitarity to the presence of derivatives in the
operators describing the angular momentum and reproduce the result
of~\cite{Manohar:2022dea} obtained by resumming the smallvelocity
expansion. As a new application, we derive also the variation in each
particle's angular momentum up to 3PM: calculating separately field and
particle contributions allows us to check the balance laws explicitly. We
also show how the eikonal operator encodes the linearresponse formula of
BiniDamour by deriving the linear radiationreaction contribution to the
transverse impulse at 4PM. 
Towards equivariant YangMills theory
Authors: Francesco Bonechi, Alberto S. Cattaneo, Maxim Zabzine
Preprint number: UUITP41/22
We study four dimensional gauge theories in the context of an equivariant extension of the BatalinVilkovisky (BV) formalism. We discuss the embedding of BV YangMills (YM) theory into a larger BV theory and their relation. Partial integration in the equivariant BV setting (BV pushforward map) is performed explicitly for the abelian case. As result, we obtain a nonlocal homological generalization of the Cartan calculus and a nonlocal extension of the abelian YM BV action which satisfies the equivariant master equation.

Back to Heterotic Strings on ALE Spaces: Part I  Instantons, 2groups and Tduality
Authors: Michele Del Zotto, Muyang Liu, PaulKonstantin Oehlmann
Preprint number: UUITP40/22
Abstract: In this paper we begin revisiting the little string theories (LSTs) which govern the dynamics of the instantonic heterotic $E_8 \times E_8$ fivebranes probing ALE singularities, building on and extending previous results on the subject by Aspinwall and Morrison as well as Blum and Intriligator. Our focus are the cases corresponding to choices of nontrivial flat connections at infinity. The latter are in particular interesting for the exceptional ALE singularities, where a brane realization in Type I$'$ is lacking. Our approach to determine these models is based on 6d conformal matter: we determine these theories as generalized 6d quivers. All these LSTs have a higherone form symmetry which forms a 2group with the zeroform Poincar\'e symmetry, the Rsymmetry and the other global symmetries: the matching of the Rsymmetry twogroup structure constant is a stringent constraint for Tdualities, which we use in combination with the matching of 5d Coulomb branches and flavor symmetries upon circle reduction, as a consistency check for the realization of the 6d LSTs we propose.

N^3LO QuadraticinSpin Interactions for Generic Compact Binaries
Authors: JungWook Kim, Michèle Levi, Zhewei Yin
Preprint number: UUITP39/22
We derive the third subleading (N^3LO) corrections in the quadraticinspin sectors via the EFT of spinning objects in postNewtonian (PN) gravity. These corrections include contributions from 4 sectors for generic compact objects, entering at the fifth PN order. One of these is a new tidal interaction, first entering in the spinning sectors, which complements the tidal interaction that first enters at the same PN order in the nonspinning sector. The evaluation of Feynman graphs is carried out in a generic dimension via multiloop methods, and yields dimensionalregularization poles in conjunction with logarithms. At these higherspin sectors the reduction of generalized Lagrangians entails redefinitions of the position beyond linear order. We provide here for the first time the relevant Lagrangians and Hamiltonians, and their useful simplified versions. We also derive the consequent gaugeinvariant binding energy relations to the angular momentum and frequency. We end with a derivation of all scattering angles for aligned spins that correspond to an extension of the Hamiltonians for binary inspirals of the 4 independent sectors, and find complete agreement with the limited available results obtained via traditional GR, EFT and scatteringamplitudes methods.

The phase diagram of TTdeformed YangMills theory on the sphere
Authors: Luca Griguolo, Rodolfo Panerai, Jacopo Papalini, Domenico Seminara
Preprint number: UUITP38/22
We study the largeN dynamics of TTdeformed twodimensional YangMills theory at genus zero. The 1/Nexpansion of the free energy is obtained by exploiting the associated flow equation and the complete phase diagram of the theory is derived for both signs of the rescaled deformation parameter τ. We observe a thirdorder phase transition driven by instanton condensation, which is the deformed version of the familiar DouglasKazakov transition separating the weaklycoupled from the stronglycoupled phase. By studying said phases we compute the deformation of both the perturbative sector and the GrossTaylor string expansion. Nonperturbative corrections in τ drive the system into an unexplored disordered phase separated by a novel critical line meeting tangentially the DouglasKazakov one at a tricritical point. The associated phase transition is induced by the collision of largeN saddle points, determining its secondorder character.

Modular graph forms from equivariant iterated Eisenstein integrals
Authors: Daniele Dorigoni, Mehregan Doroudiani, Joshua Drewitt, Martijn Hidding, Axel Kleinschmidt, Nils Matthes, Oliver Schlotterer and Bram Verbeek
Preprint number: UUITP37/22
The lowenergy expansion of closedstring scattering amplitudes at genus one introduces infinite families of nonholomorphic modular forms dubbed ``modular graph forms''. Their differential and numbertheoretic properties motivated Brown's alternative construction of nonholomorphic modular forms in the recent mathematics literature from socalled ``equivariant iterated Eisenstein integrals''. In this work, we provide the first validations beyond depth one of Brown's conjecture that equivariant iterated Eisenstein integrals contain modular graph forms. Apart from a variety of examples at depth two and three, we spell out the systematics of the dictionary and make certain elements of Brown's construction fully explicit to all orders.

Spinning correlators in N = 2 SCFTs: Superspace and AdS amplitudes
Authors: Agnese Bissi, Giulia Fardelli, Andrea Manenti, Xinan Zhou
Preprint number: UUITP36/22
Abstract: We study fourpoint functions of spinning operators in the flavor current multiplet in four dimensional N = 2 SCFTs, using superspace techniques. In particular we explicitly construct the differential operators relating the different components of the supercorrelator. As a byproduct of our analysis, we report the computation of the fourpoint amplitudes of gluons in bosonic YangMills theories on AdS5 and we give evidence of an AdS double copy relation between the gluon amplitude and its gravitational counterpart.

N^3LO SpinOrbit Interaction via the EFT of Spinning Gravitating Objects
Authors: JungWook Kim, Michèle Levi, Zhewei Yin
Preprint number: UUITP35/22
Abstract: We present the derivation of the nexttonexttonexttoleading order (N^3LO) spinorbit interaction at the state of the art of postNewtonian (PN) gravity via the Effective Field Theory of spinning objects. The present sector contains the largest and most elaborate collection of Feynman graphs ever tackled to date in spin sectors, and in all PN sectors up to third subleading order. Our computations are carried out via advanced multiloop methods, and their most demanding aspect is the imperative transition to a generic dimension across the whole derivation, which is common to sectors as of the N^3LO. At this high order of sectors with spin it is also needed to extend the formal procedure for the reduction of higherorder time derivatives of spin variables – beyond linear order – for the first time. The full interaction potentials in Lagrangian and Hamiltonian forms are provided here for the first time. These enable, e.g. the direct derivation of equations of motion for both the position and spin, studies of the related Poincaré algebra, or explorations of various possible effectiveonebody models. The consequent gaugeinvariant observables are also derived, namely relations among the binding energy, angular momentum, and orbital frequency. Complete agreement is found with the binding energy for circular orbits derived via traditional GR methods. In contrast to the latter derivation, the framework here is freestanding and generic, and provides independent derivations and results, which are critical to carefully establish the state of the art, and keep pushing the present highorder precision frontier.

Elliptic modular graph forms II: Iterated integrals
Authors: Martijn Hidding, Oliver Schlotterer, Bram Verbeek
Preprint number: UUITP34/22
Abstract: Elliptic modular graph forms (eMGFs) are nonholomorphic modular forms depending on a modular parameter $\tau$ of a torus and marked points $z$ thereon. Traditionally, eMGFs are constructed from nested lattice sums over the discrete momenta on the worldsheet torus in closedstring genusone amplitudes. In this work, we develop methods to translate the latticesum realization of eMGFs into iterated integrals over modular parameters $\tau$ of the torus with particular focus on cases with one marked point. Such iteratedintegral representations manifest algebraic and differential relations among eMGFs and their degeneration limit $\tau \rightarrow i\infty$. From a mathematical point of view, our results yield concrete realizations of singlevalued elliptic polylogarithms at arbitrary depth in terms of meromorphic iterated integrals over modular forms and their complex conjugates. The basis dimensions of eMGFs at fixed modular and transcendental weights are derived from a simple counting of iterated integrals and a generalization of Tsunogai's derivation algebra.

Yano F structures and extended Supersymmetry
Authors: Ulf Lindström
Preprint number: UUITP33/22
It is described how extended supersymmetry realised directly on the (2, 2) semichiral superfields of a symplectic sigma model gives rise to a geometry on the doubled tangent bundle consisting of two Yano F structures on a parahermitian manifold. Closure of the algebra and invariance of the action is discussed in this framework and integrability of the F structures is defined and shown to hold. The reduction to the usual (1, 1) sigma model description and identification with the biquaternionic set of complex structures and their properties is described. The F structure formulation should be applicable to many other models and will have an equivalent formulation in Generalised Geometry.

Sevendimensional super YangMills at negative coupling
Authors: Joseph A. Minahan, Usman Naseer, and Charles Thull
Preprint number: UUITP32/22
We consider the partition function for Euclidean $SU(N)$ super YangMills on a squashed sevensphere. We show that the localization locus of the partition function has instanton membrane solutions wrapping the six ``fixed" threespheres on the $\mathbb{S}^7$. The ADHM variables of these instantons are fields living on the membrane world volume. We compute their contribution by localizing the resulting threedimensional supersymmetric field theory. In the roundsphere limit the individual instanton contributions are singular, but the singularities cancel when adding the contributions of all six threespheres.
The full partition function on the ${\mathbb S}^7$ is welldefined even when the square of the effective YangMills coupling is negative. We show for an $SU(2)$ gauge theory in this regime that the bare negative tension of the instanton membranes is canceled off by contributions from the instanton partition function, indicating the existence of tensionless membranes. We provide evidence that the low energy phase in this regime is distinct from the usual weakly coupled super YangMills and, in fact, is gravitational.

Feynman parameter integration through differential equations
Authors: Martijn Hidding, Johann Usovitsch
Preprint number: UUITP31/22
We present a new method for numerically computing generic multiloop Feynman integrals. The method relies on an iterative application of Feynman's trick for combining two propagators. Each application of Feynman's trick introduces a simplified Feynman integral topology which depends on a Feynman parameter that should be integrated over. For each integral family, we set up a system of differential equations which we solve in terms of a piecewise collection of generalized series expansions in the Feynman parameter. These generalized series expansions can be efficiently integrated term by term, and segment by segment. This approach leads to a fully algorithmic method for computing Feynman integrals from differential equations, which does not require the manual determination of boundary conditions. Furthermore, the most complicated topology that appears in the method often has less master integrals than the original one. We illustrate the strength of our method with a fivepoint twoloop integral family.

Classical Limit of HigherSpin String Amplitudes
Authors: Lucile Cangemi, Paolo Pichini
Preprint number: UUITP30/22
Abstract: It has been shown that a special set of threepoint amplitudes between
two massive spinning states and a graviton reproduces the linearised stressenergy
tensor for a Kerr black hole in the classical limit. In this work we revisit this result
and compare it to the analysis of the amplitudes describing the interaction of leading
Regge states of the open and closed superstring. We find an allspin result for the
classical limit of two massive spinning states interacting with a photon or graviton.
This result differs from Kerr and instead matches the current fourvector and the
stressenergy tensor generated by a classical string coupled to electromagnetism and
gravity respectively. For the superstring amplitudes, contrary to
the blackhole case, we find that the spin to infinity limit is necessary to generate
the correct classical spin multipoles. 
Nexttoleadingorder QCD Corrections to Higgs Production in association with a Jet
Authors: R. Bonciani, V. Del Duca, H. Frellesvig, M. Hidding, V. Hirschi, F. Moriello, G. Salvatori, G. Somogyi, F. Tramontano
Preprint number: UUITP29/22
We compute the nexttoleadingorder (NLO) QCD corrections to the Higgs pT distribution in Higgs production in association with a jet via gluon fusion at the LHC, with exact dependence on the mass of the quark circulating in the heavyquark loops. The NLO corrections are presented including the topquark mass, and for the first time, the bottomquark mass as well. Further, besides the onshell mass scheme, we consider for the first time a running mass renormalisation scheme. The computation is based on amplitudes which are valid for arbitrary heavyquark masses.

Geometry, conformal KillingYano tensors and conserved “currents”
Authors: Ulf Lindström and Özgür Sar{\i}o\u{g}lu
Preprint number: UUITP28/22
Abstract: In this brief letter we derive some useful identities relating conformal KillingYano tensors (CKYTs) and geometric quantities. We then use these identities to construct covariantly conserved “currents”. We conclude that rank$n$ currents linear in rank$n$ CKYTs $k$ and second order in derivatives must have a simple form in terms of $dk$. Using the Pleba\'nskiDemia\'nski and the KerrNewman metrics, we show how these currents can be used to define charges. By construction, these currents are covariant under a general conformal rescaling of the metric.

On the 6d Origin of Noninvertible Symmetries in 4d
Authors: Vladimir Bashmakov, Michele Del Zotto, Azeem Hasan
Preprint number: UUITP27/22
It is wellknown that sixdimensional superconformal field theories can be exploited to unravel interesting features of lowerdimensional theories obtained via compactifications. In this short note we discuss a new application of 6d (2,0) theories in constructing 4d theories with KramersWannierlike noninvertible symmetries. Our methods allow to recover previously known results, as well as to exhibit infinitely many new examples of four dimensional theories with "Mality" defects (arising from operations of order M, generalizing dualities). In particular, we obtain examples of order M=p^k, where p>1 is a prime number and k is a positive integer.

Overextremal brane shells from string theory?
Authors: Ulf Danielsson, Vincent Van Hemelryck and Thomas Van Riet
Preprint Number: UUITP26/22
Abstract: We demonstrate that, if the usual phenomenological compactifications of IIB string theory with warped throats and antibranes make sense, there must exist spherical brane shells in 4d that are overcharged. They correspond to classical overextremal objects but without the usual naked singularities. The objects are made from D3 particles that puff into spherical 5branes that stabilise at finite radii in 4d and whose inside corresponds to the supersymmetric AdS vacuum. One can think of these shells as stabilised BrownTeitelboim bubbles. We find that these objects can be significantly larger than the string scale depending on the details of the warped compactification.

Numerical Metrics for Complete Intersection and KreuzerSkarke CalabiYau Manifolds
Authors: Magdalena Larfors, Andre Lukas, Fabian Ruehle, Robin Schneider
Preprint number: UUITP25/22
We introduce neural networks to compute numerical Ricciflat CY metrics for complete intersection and KreuzerSkarke CalabiYau manifolds at any point in Kähler and complex structure moduli space, and introduce the package cymetric which provides computation realizations of these techniques. In particular, we develop and computationally realize methods for pointsampling on these manifolds. The training for the neural networks is carried out subject to a custom loss function. The Kähler class is fixed by adding to the loss a component which enforces the slopes of certain line bundles to match with topological computations. Our methods are applied to various manifolds, including the quintic manifold, the bicubic manifold and a KreuzerSkarke manifold with Picard number two. We show that volumes and line bundle slopes can be reliably computed from the resulting Ricciflat metrics. We also apply our results to compute an approximate HermitianYangMills connection on a specific line bundle on the bicubic.

Classical gravitational spinningspinless scattering at $\mathcal{O}(G^2S^\infty)$
Authors: Rafael Aoude, Kays Haddad, Andreas Helset
Preprint number: UUITP24/22
Making use of the recentlyderived, allspin, oppositehelicity Compton amplitude, we calculate the classical gravitational scattering amplitude for one spinning and one spinless object at $\mathcal{O}(G^2)$ and all orders in spin. By construction, this amplitude exhibits the spin structure that has been conjectured to describe Kerr black holes. This spin structure alone is not enough to fix all deformations of the Compton amplitude by contact terms, but when combined with considerations of the ultrarelativistic limit we can uniquely assign values to the parameters remaining in the eveninspin sector. Once these parameters are determined, much of the spin dependence of the amplitude resums into hypergeometric functions. Finally, we derive the eikonal phase for alignedspin scattering.

Gauge invariance from onshell massive amplitudes and tree unitarity
Authors: Da Liu, Zhewei Yin
Preprint number: UUITP23/22
We study the threeparticle and fourparticle scattering amplitudes for an arbitrary, finite number of massive scalars, spinors and vectors by employing the onshell massive spinor formalism. We consider the most general threeparticle amplitudes with energy growing behavior at most of O(E). This is the special case of the requirement of tree unitarity, which states that the Nparticle scattering amplitudes at treelevel should grow at most as O(E^(4N)) in the high energy hard scattering limit, i.e. at fixed nonzero angles. Then the factorizable parts of the fourparticle amplitudes are calculated by gluing the onshell threeparticle amplitudes together and utilizing the fact that treelevel amplitudes have only simple poles. The contact parts of the fourparticle amplitudes are further determined by tree unitarity, which also puts strong constraints on the possible allowed threeparticle coupling constants and the masses. The derived relations among them converge to the predictions of gauge invariance in the UV theory. This provides a purely onshell understanding of spontaneously broken gauge theories.

Global Structures from the Infrared
Authors: Michele Del Zotto and Iñaki García Etxebarria
Preprint number: UUITP22/22
Abstract: Quantum field theories with identical local dynamics can admit different choices of global structure, leading to different partition functions and spectra of extended operators. Such choices can be reformulated in terms of a topological field theory in one dimension higher, the symmetry TFT. In this paper we show that this TFT can be reconstructed from a careful analysis of the infrared Coulomblike phases. In particular, the TFT matches between the UV and the IR. This provides a purely field theoretical counterpart of several recent results obtained via geometric engineering in various string/M/F theory setups for theories in four and five dimensions that we confirm and extend.

Snowmass White Paper: the DoubleCopy and its Applications
Authors: Tim Adamo, John Joseph M. Carrasco, Mariana CarrilloGonzález, Marco Chiodaroli, Henriette Elvang, Henrik Johansson, Donal O'Connell, Radu Roiban, Oliver Schlotterer
Preprint number: UUITP21/22
The doublecopy is, in essence, a map between scattering amplitudes in a broad variety of familiar field and string theories. In addition to the mathematically rich intrinsic structure, it underlies a multitude of active research directions and has a range of interesting applications in quantum, classical and effective field theories, including broad topics such as string theory, particle physics, astrophysics, and cosmology. This Snowmass White Paper provides a brief introduction to the doublecopy, its applications, current research and future challenges.

The eikonal operator at arbitrary velocities I: the softradiation limit
Authors: Paolo Di Vecchia, Carlo Heissenberg, Rodolfo Russo, Gabriele Veneziano
Preprint: UUITP20/22
Abstract: Observables related to the real part of the gravitational eikonal, such as the deflection angle and time delay, have been found so far to have a smooth postMinkowskian (PM) expansion whose validity extends from the nonrelativistic to the most extreme ultrarelativistic (UR) regime, which smoothly connects with massless particle collisions. To describe gravitational radiation, the eikonal phase has to be promoted to a unitary operator for which we motivate a proposal and start discussing properties in the softradiation limit. A convergent PM expansion is found to only hold below an UR bound (discussed in the GR literature in the seventies) above which a different expansion is instead needed implying, in general, some nonanalyticity in Newton's constant. In this extreme UR regime soft radiative observables receive contributions only from gravitons and are therefore universal. This generalises the pattern discussed in~\cite{DiVecchia:2020ymx} beyond the elastic case.

Radiation reaction for spinning blackhole scattering
Authors: Francesco Alessio, Paolo Di Vecchia
Preprint: UUITP19/22
Abstract: Starting from the leading soft term of the 5point amplitude, involving a graviton and two Kerr black holes, that factorises into the product of the elastic amplitude without the graviton and the leading soft factor, we compute the infrared divergent contribution to the imaginary part of the twoloop eikonal. Then, using analyticity and crossing symmetry, we determine the radiative contribution to the real part of the twoloop eikonal and from it the radiative part of the deflection angle for spins aligned to the orbital angular momentum, the loss of angular momentum and the zero frequency limit of the energy spectrum for any spin and for any spin orientation. For spin one we find perfect agreement with recent results obtained with the supersymmetric worldline formalism.

The SAGEX Review on Scattering Amplitudes Chapter 2: An Invitation to ColorKinematics Duality and the Double Copy
Authors: Zvi Bern, John Joseph Carrasco, Marco Chiodaroli, Henrik Johansson, Radu Roiban
Preprint: UUITP18/22
Abstract: Advances in scattering amplitudes have exposed previouslyhidden colorkinematics and doublecopy structures in theories ranging from gauge and gravity theories to effective field theories such as chiral perturbation theory and the BornInfeld model. These novel structures both simplify higherorder calculations and pose tantalizing questions related to a unified framework underlying relativistic quantum theories. This introductory minireview article invites further exploration of these topics. After a brief introduction to colorkinematics duality and the double copy as they emerge at tree and looplevel in gauge and gravity theories, we present two distinct examples: 1) an introduction to the web of doublecopyconstructible theories, and 2) a discussion on the application of the double copy to calculations relevant to gravitationalwave physics.

2Group Symmetries and MTheory
Authors: Michele Del Zotto, Iñaki García Etxebarria, Sakura SchäferNameki
Preprint: UUITP17/22
Quantum Field Theories engineered in Mtheory can have 2group symmetries, mixing 0form and 1form symmetry backgrounds in nontrivial ways. In this paper we develop methods for determining the 2group structure from the boundary geometry of the Mtheory background. We illustrate these methods in the case of 5d theories arising from Mtheory on ordinary and generalised toric CalabiYau cones, including cases in which the resulting theory is nonLagrangian. Our results confirm and elucidate previous results on 2groups from geometric engineering.

Angular momentum of zerofrequency gravitons
Authors: Paolo Di Vecchia, Carlo Heissenberg, Rodolfo Russo
Preprint: UUITP16/22
By following closely Weinberg's soft theorem, which captures the $1/\omega$ pole contribution to the amplitude for soft graviton emissions ($\omega<\Lambda$) on top of an arbitrary background hard process, we calculate the expectation value of the graviton's angular momentum operator for arbitrary collisions dressed with soft radiation. We find that the result becomes independent of the cutoff $\Lambda$ on the graviton's frequency, effectively localizing at $\omega=0$. In this way, our result captures the contribution to the angular momentum that comes from the zerofrequency modes. Like the soft theorem, our formula has an exact dependence on the kinematics of the hard particles and is only a function of their momenta.
As an example, we discuss in some detail the case of the $2 \to 2$ scattering of spinless particles in General Relativity and ${\cal N}=8$ supergravity. 
Exact TT deformation of twodimensional Maxwell theory
Authors: Luca Griguolo, Rodolfo Panerai, Jacopo Papalini, Domenico Seminara
Preprint: UUITP15/22
TTdeformed twodimensional quantum Maxwell theory on the torus is examined, taking into account nonperturbative effects in the deformation parameter μ. We study the deformed partition function solving the relevant flow equation at the level of individual flux sectors. Summing exactly the “instanton” series, we obtain a welldefined expression for the partition function at arbitrary μ. For μ > 0, the quantum spectrum of the theory experiences a truncation, the partition function reducing to a sum over a finite set of positiveenergy states. For μ < 0 instead, the appearance of nonperturbative contributions in μ drastically modifies the structure of the partition function, regularizing its naive divergences through instantonlike subtractions. For each flux sector, we show that the semiclassical contribution is dominated by the deformed classical action. The theory is observed to undergo infiniteorder phase transitions for certain values of μ, associated with the vanishing of Polyakovloop correlators.

Openstring integrals with multiple unintegrated punctures at genus one
Authors: André Kaderli and Carlos Rodriguez
Preprint number: UUITP14/22
We study integrals appearing in intermediate steps of oneloop openstring amplitudes, with multiple unintegrated punctures on the $A$cycle of a torus. We construct a vector of such integrals which closes after taking a total differential with respect to the $N$ unintegrated punctures and the modular parameter $\tau$. These integrals are found to satisfy the elliptic KnizhnikZamolodchikovBernard (KZB) equations, and can be written as a power series in $\alpha$'  the string length squared  in terms of elliptic multiple polylogarithms (eMPLs). In the $N$puncture case, the KZB equation reveals a representation of $B_{1,N}$, the braid group of $N$ strands on a torus, acting on its solutions. We write the simplest of these braid group elements  the braiding one puncture around another  and obtain generating functions of analytic continuations of eMPLs. The KZB equations in the socalled universal case is written in terms of the genusone DrinfeldKohno algebra $\mathfrak{t}_{1,N} \rtimes \mathfrak{d}$, a graded algebra. Our construction determines matrix representations of various dimensions for several generators of this algebra which respect its grading up to commuting terms.

Snowmass White Paper: String Perturbation Theory
Authors: Nathan Berkovits, Eric D'Hoker, Michael B. Green, Henrik Johansson, Oliver Schlotterer
Preprint number: UUITP13/22
Abstract: The purpose of this White Paper is to review recent progress towards elucidating and evaluating string amplitudes, relating them to quantum field theory amplitudes, applying their predictions to string dualities, exploring their connection with gravitational physics, and deepening our understanding of their mathematical structure. We also present a selection of targets for future research.

Searching for Kerr in the 2PM amplitude
Authors: Rafael Aoude, Kays Haddad, Andreas Helset
Preprint number: UUITP12/22
Abstract: The classical scattering of spinning objects is well described by the spinorhelicity formalism for heavy particles. Using these variables, we derive spuriouspolefree, oppositehelicity Compton amplitudes (factorizing on physical poles to the minimal, allspin threepoint amplitudes of ref. [1]) in the classical limit for QED, QCD, and gravity. The cured amplitudes are subject to deformations by contact terms, the vast majority of whose contributions we can fix by imposing a relation between spin structuresmotivated by lower spin multipoles of black hole scatteringat the second postMinkowskian (2PM) order. For QED and gravity, this leaves a modest number of unfixed coefficients parametrizing contactterm deformations, while the QCD amplitude is uniquely determined. Our gravitational Compton amplitude allows us to push the stateoftheart of spinning2PM scattering to any order in the spin vectors of both objects; we present results here and in the auxiliary file 2PMSpin8Aux.nb up to eighth order in the spin vectors. Interestingly, despite leftover coefficients in the Compton amplitude, imposing the aforementioned relation between spin structures uniquely fixes some higherspin parts of the 2PM amplitude.

Functions Beyond Multiple Polylogarithms for Precision Collider Physics
Authors: Jacob Bourjaily, Johannes Broedel, Ekta Chaubey, Claude Duhr, Hjalte Frellesvig, Martijn Hidding, Robin Marzucca, Andrew McLeod, Marcus Spradlin, Lorenzo Tancredi, Cristian Vergu, Matthias Volk, Anastasia Volovich, Matt von Hippel, Stefan Weinzierl, Matthias Wilhelm, Chi Zhang.
Preprint number: UUITP11/22
Abstract: Feynman diagrams constitute one of the essential ingredients for making precision predictions for collider experiments. Yet, while the simplest Feynman diagrams can be evaluated in terms of multiple polylogarithms  whose properties as special functions are well understood  more complex diagrams often involve integrals over complicated algebraic manifolds. Such diagrams already contribute at NNLO to the selfenergy of the electron, $t \bar{t}$ production, $\gamma \gamma$ production, and Higgs decay, and appear at two loops in the planar limit of maximally supersymmetric YangMills theory. This makes the study of these more complicated types of integrals of phenomenological as well as conceptual importance. In this white paper contribution to the Snowmass community planning exercise, we provide an overview of the state of research on Feynman diagrams that involve special functions beyond multiple polylogarithms, and highlight a number of research directions that constitute essential avenues for future investigation.

2d Sigma Models and Geometry
Authors: Ulf Lindström
Preprint number: UUITP10/22
Supersymmetric nonlinear sigma models have target spaces that carry interesting geometry. The geometry is richer the more supersymmetries the model has. The study of models with two dimensional world sheets is particularly rewarding since they allow for torsionful geometries. In this review I describe and exemplify the relation of $2d$ supersymmetry to Riemannian, complex, bihermitian, $(p,q)$ hermitean, Kähler, hyperkähler, generalised geometry and more.

Localizing nonlinear $N=(2,2)$ sigma model on $S^2$
Authors: Victor Alekseev, Guido Festuccia, Victor Mishnyakov, Nicolai Terziev and Maxim Zabzine
Preprint number: UUITP09/22
We present a systematic study of ${\cal N}=(2,2)$ supersymmetric nonlinear sigma models on $S^2$ with the target being a Kähler manifold. We discuss their reformulation in terms of cohomological field theory. In the cohomological formulation we use a novel version of 2D selfduality which involves a $U(1)$ action on $S^2$. In addition to the generic model we discuss the theory with target space equivariance corresponding to a supersymmetric sigma model coupled to a nondynamical supersymmetric background gauge multiplet. We discuss the localization locus and perform a oneloop calculation around the constant maps. We argue that the theory can be reduced to some exotic model over the moduli space of holomorphic disks.

Spinorhelicity formalism for massive and massless amplitudes in five dimensions
Authors: Marco Chiodaroli, Murat Günaydin, Henrik Johansson and Radu Roiban
Preprint Number: UUITP08/22
Fivedimensional gauge and gravity theories are known to exhibit striking properties. D=5 is the lowest dimension where massive tensor states appear naturally, providing a testing ground for perturbative insights into sixdimensional tensor theories. Fivedimensional supergravities are highly constrained and admit elegant geometric and algebraic formulations, with global symmetries manifest at the Lagrangian level. In this paper, we take a step towards the systematic investigation of amplitudes in five dimensions, and present a fivedimensional version of the spinorhelicity formalism, applicable to massless, massive and supersymmetric states. We give explicit representations for onshell spinor and polarization variables such that the littlegroup symmetry and gauge redundancy are manifest. Massive selfdual tensor states are discussed in some detail, as well as all the onshell supermultiplets that can appear in mattercoupled gauge and supergravity theories. As a byproduct of considering supersymmetry in the presence of central charge, we obtain massless tendimensional MajoranaWeyl spinors as products of fivedimensional massive spinors.

Uses of Killing and KillingYano Tensors
Authors: Ulf Lindström and Özgür Sarıoğlu
Preprint Number: UUITP07/22
In this contribution we have collected some facts about Killing and KillingYano tensors that we feel are of general interest for researchers working on problems that rely on differential geometry. We also include some of our recent studies pertaining to currents, charges and (super)invariants for particles and tensionless strings.

Tensionless Strings and Killing(Yano) Tensors
Authors: Ulf Lindström and Özgür Sarıoğlu
Preprint Number: UUITP06/22
We construct invariants for bosonic and spinning tensionless (null) strings in back grounds that carry Killing or KillingYano tensors of mixed type. This is facilitated by the close relation of these strings to point particles. We apply the construction to the Minkowski and to the KerrNewman background. 
A tale of tails through generalized unitarity
Authors: Alex Edison, Michèle Levi
Preprint Number: UUITP05/22
We introduce a novel framework to study highorder gravitational effects on a binary from the scattering of its emitted gravitational radiation. Here we focus on the radiationreaction due to the background of the binary’s gravitational potential, namely on the socalled tail effects. We start from the effective field theory of a binary composite particle, and through multiloop and generalized unitarity methods, we derive the effective action of the dynamical multipoles, the energy spectrum, and the observable flux due to these effects. We proceed through the third subleading such radiationreaction effect – at the fourloop level and the seventh order in postNewtonian gravity – shedding new light on the higherorder effects, and completing the state of the art.

Oneloop amplitudes in EinsteinYangMills from forward limits
Authors: Franziska Porkert, Oliver Schlotterer
Preprint number: UUITP04/22
We present a method to compute the integrands of oneloop EinsteinYangMills amplitudes for any number of external gauge and gravity multiplets. Our construction relies on the doublecopy structure of EinsteinYangMills as (super)YangMills with the socalled YM+phi^3 theory  pure YangMills coupled to biadjoint scalars  which we implement via oneloop CachazoHeYuan formulae. The YM+phi^3 building blocks are obtained from forward limits of treelevel input in external gluons and scalars, and we give the composition rules for any number of traces and orders in the couplings g and kappa. One the one hand, we spell out supersymmetry and dimensionagnostic relations that reduce loop integrands of EinsteinYangMills to those of pure gauge theories. On the other hand, we present fourpoint results for maximal and halfmaximal supersymmetry where all supersymmetry cancellations are exposed. In the halfmaximal case, we determine sixdimensional anomalies due to chiral hypermultiplets in the loop.