Preprints 2022

Authors: Adam Chalabi, Christopher P. Herzog, Krishnendu Ray, Brandon Robinson, Jacopo Sisti, Andreas Stergiou

Preprint number: UUITP-53/22

Authors: Ulf Lindström  and Özgür  Sarıoğlu

Preprint number: UUITP-52/22

Authors: Eric D'Hoker, Martijn Hidding and Oliver Schlotterer

Preprint number: UUITP-51/22

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 four-point function. Of particular importance are certain trilinear relations that we shall define and prove. In a second step, the known expressions for the genus-two 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 two-point function. The hyper-elliptic formulation of genus-two 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 theta-functions, and applications to the evaluation of higher-point string amplitudes, are relegated to subsequent companion papers.

Authors: Vladimir Bashmakov, Azeem Hasan, Michele Del Zotto, Justin Kaidi

Preprint number: UUITP-50/22

Abstract: We study the non-invertible 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 non-invertible symmetry is intrinsic, i.e. whether it can be related to an invertible symmetry by discrete gauging. We then describe the higher-dimensional origin of our results, and explain how the Anomaly and Symmetry TFTs, as well as N-ality defects, of class S theories can be obtained from compactification of a 7d Chern-Simons theory. Interestingly, we find that the Symmetry TFT for theories with intrinsically non-invertible symmetries can only be obtained by coupling the 7d Chern-Simons theory to topological gravity.

Authors: Ulf Danielsson, Oscar Henriksson, Daniel Panizo

Preprint number: UUITP-49/22

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.

Authors: Michèle Levi, Roger Morales, Zhewei Yin

Preprint number: UUITP-48/22

In this paper we confirm the generalized actions of the complete NLO cubic-in-spin 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 spin-orbit sector recently derived within our approach. We also derive the binding energies with gauge-invariant relations useful for gravitational-wave applications. Finally, we derive the extrapolated scattering angles in the aligned-spins case, and we find complete agreement with previous results derived for the scattering of black holes via scattering-amplitudes 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.

Authors: Alex Edison and Micah Tegevi

Preprint number: UUITP-47/22

The alpha'-expansion of string theory provides a rich set of higher-dimension operators, indexed by zeta values, which can be used to study color-kinematics duality and the double copy. These two powerful properties, actually first noticed in tree-level 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 color-kinematics dual numerators at one loop and four points for insertions of operator combinations corresponding to the lowest four zeta_2-free 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 color-dual representation related to the regularization of bubble-on-external-leg type diagrams. The simplest regularization approach leads to an overconstrained system, signaling an incompatibility between the chosen regularization and color-kinematics duality. Using the constructed color-dual numerators, we find two different Bern-Carrasco-Johansson double copies that produce candidate closed-string-insertion 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 double-copy numerator definitions.

Author: Carlo Heissenberg

Preprint number: UUITP-46/22

We calculate the tidal corrections to the loss of angular momentum in a two-body collision at leading Post-Minkowskian order from an amplitude-based approach. The eikonal operator allows us to efficiently combine elastic and inelastic amplitudes, and captures both the contributions due to genuine gravitational-wave emissions and those due to the static gravitational field. We calculate the former by harnessing powerful collider-physics techniques such as reverse-unitarity, thereby reducing them to cut two-loop integrals, and validate the result with an independent calculation in the Post-Newtonian limit. For the latter, we can employ the results of arXiv:2203.11915 where static-field effects were calculated for generic gravitational scattering events using the leading soft graviton theorem.

Authors: Alex Edison, Song He, Henrik Johansson, Oliver Schlotterer, Fei Teng, Yong Zhang

Preprint number: UUITP-45/22

We take a major step towards computing D-dimensional one-loop amplitudes in general gauge theories, compatible with the principles of unitarity and the color-kinematics duality. For n-point amplitudes with either supersymmetry multiplets or generic non-supersymmetric matter in the loop, simple all-multiplicity expressions are obtained for the maximal cuts of kinematic numerators of n-gon diagrams. At n=6,7 points with maximal supersymmetry, we extend the cubic-diagram numerators to encode all contact terms, and thus solve the long-standing problem of \emph{simultaneously} realizing the following properties: color-kinematics 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. Color-kinematics dual representations with similar properties are presented in the half-maximally supersymmetric case at n=4,5 points. The resulting gauge-theory integrands and their supergravity counterparts obtained from the double copy are checked to reproduce the expected ultraviolet divergences.

Authors: Carlos R. Mafra and Oliver Schlotterer

Preprint number: UUITP-44/22

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 color-kinematics duality in field theory and the mathematical structure of alpha'-corrections.

Authors: Ulf Lindström and Özgur Sarioglu

Preprint number: UUITP-43/22

Authors: Paolo Di Vecchia, Carlo Heissenberg, Rodolfo Russo, Gabriele Veneziano

Preprint number: UUITP-42/22

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,
zero-frequency modes are added in order to recover the effects of a static
gravitational field. We first calculate the radiated energy-momentum 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 small-velocity
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 linear-response formula of
Bini-Damour by deriving the linear radiation-reaction contribution to the
transverse impulse at 4PM.

Authors: Francesco Bonechi, Alberto S. Cattaneo, Maxim Zabzine

Preprint number: UUITP-41/22

We study four dimensional gauge theories in the context of an equivariant extension of the Batalin-Vilkovisky (BV) formalism. We discuss the embedding of BV Yang-Mills (YM) theory into a larger BV theory and their relation. Partial integration in the equivariant BV setting (BV push-forward map) is performed explicitly for the abelian case. As result, we obtain a non-local homological generalization of the Cartan calculus and a non-local extension of the abelian YM BV action which satisfies the equivariant master equation. 

Authors: Michele Del Zotto, Muyang Liu, Paul-Konstantin Oehlmann

Preprint number: UUITP-40/22

Abstract: In this paper we begin revisiting the little string theories (LSTs) which govern the dynamics of the instantonic heterotic $E_8 \times E_8$ five-branes 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 non-trivial 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 higher-one form symmetry which forms a 2-group with the zero-form Poincar\'e symmetry, the R-symmetry and the other global symmetries: the matching of the R-symmetry two-group structure constant is a stringent constraint for T-dualities, 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.

Authors: Jung-Wook Kim, Michèle Levi, Zhewei Yin

Preprint number: UUITP-39/22

We derive the third subleading (N^3LO) corrections in the quadratic-in-spin sectors via the EFT of spinning objects in post-Newtonian (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 non-spinning sector. The evaluation of Feynman graphs is carried out in a generic dimension via multi-loop methods, and yields dimensional-regularization poles in conjunction with logarithms. At these higher-spin 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 gauge-invariant 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 scattering-amplitudes methods.

Authors: Luca Griguolo, Rodolfo Panerai, Jacopo Papalini, Domenico Seminara

Preprint number: UUITP-38/22

We study the large-N dynamics of TT-deformed two-dimensional Yang-Mills theory at genus zero. The 1/N-expansion 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 third-order phase transition driven by instanton condensation, which is the deformed version of the familiar Douglas-Kazakov transition separating the weakly-coupled from the strongly-coupled phase. By studying said phases we compute the deformation of both the perturbative sector and the Gross-Taylor string expansion. Nonperturbative corrections in τ drive the system into an unexplored disordered phase separated by a novel critical line meeting tangentially the Douglas-Kazakov one at a tricritical point. The associated phase transition is induced by the collision of large-N saddle points, determining its second-order character.

Authors: Daniele Dorigoni, Mehregan Doroudiani, Joshua Drewitt, Martijn Hidding, Axel Kleinschmidt, Nils Matthes, Oliver Schlotterer and Bram Verbeek

Preprint number: UUITP-37/22

The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms dubbed ``modular graph forms''. Their differential and number-theoretic properties motivated Brown's alternative construction of non-holomorphic modular forms in the recent mathematics literature from so-called ``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.

Authors: Agnese Bissi, Giulia Fardelli, Andrea Manenti, Xinan Zhou 

Preprint number: UUITP-36/22

Abstract: We study four-point 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 four-point amplitudes of gluons in bosonic Yang-Mills theories on AdS5 and we give evidence of an AdS double copy relation between the gluon amplitude and its gravitational counterpart.

Authors: Jung-Wook Kim, Michèle Levi, Zhewei Yin

Preprint number: UUITP-35/22

Abstract: We present the derivation of the next-to-next-to-next-to-leading order (N^3LO) spin-orbit interaction at the state of the art of post-Newtonian (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 multi-loop 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 higher-order 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 effective-one-body models. The consequent gauge-invariant 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 free-standing and generic, and provides independent derivations and results, which are critical to carefully establish the state of the art, and keep pushing the present high-order precision frontier.

Authors: Martijn Hidding, Oliver Schlotterer, Bram Verbeek

Preprint number: UUITP-34/22

Abstract: Elliptic modular graph forms (eMGFs) are non-holomorphic 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 closed-string genus-one amplitudes. In this work, we develop methods to translate the lattice-sum realization of eMGFs into iterated integrals over modular parameters $\tau$ of the torus with particular focus on cases with one marked point. Such iterated-integral 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 single-valued 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.

Authors: Ulf Lindström

Preprint number: UUITP-33/22

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 bi-quaternionic 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.

Authors: Joseph A. Minahan, Usman Naseer, and Charles Thull

Preprint number: UUITP-32/22

We consider the partition function for Euclidean $SU(N)$ super Yang-Mills on a squashed seven-sphere. We show that the localization locus of the partition function has instanton membrane solutions wrapping  the six ``fixed" three-spheres 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 three-dimensional supersymmetric field theory. In the round-sphere limit the individual instanton contributions are singular, but the singularities cancel when adding the contributions of all six three-spheres.

The full partition function on the ${\mathbb S}^7$ is well-defined even when the square of the effective Yang-Mills 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 Yang-Mills and, in fact, is gravitational.

Authors: Martijn Hidding, Johann Usovitsch

Preprint number: UUITP-31/22

We present a new method for numerically computing generic multi-loop 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 five-point two-loop integral family.

Authors: Lucile Cangemi, Paolo Pichini

Preprint number: UUITP-30/22

Abstract: It has been shown that a special set of three-point amplitudes between
two massive spinning states and a graviton reproduces the linearised stress-energy
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 all-spin 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 four-vector and the
stress-energy tensor generated by a classical string coupled to electromagnetism and
gravity respectively. For the superstring amplitudes, contrary to
the black-hole case, we find that the spin to infinity limit is necessary to generate
the correct classical spin multipoles.

Authors: R. Bonciani, V. Del Duca, H. Frellesvig, M. Hidding, V. Hirschi, F. Moriello, G. Salvatori, G. Somogyi, F. Tramontano

Preprint number: UUITP-29/22

We compute the next-to-leading-order (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 heavy-quark loops. The NLO corrections are presented including the top-quark mass, and for the first time, the bottom-quark mass as well. Further, besides the on-shell mass scheme, we consider for the first time a running mass renormalisation scheme. The computation is based on amplitudes which are valid for arbitrary heavy-quark masses.

Authors: Ulf Lindström and Özgür Sar{\i}o\u{g}lu

Preprint number: UUITP-28/22

Abstract: In this brief letter we derive some useful identities relating conformal Killing-Yano 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\'nski-Demia\'nski and the Kerr-Newman 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. 

Authors: Vladimir Bashmakov, Michele Del Zotto, Azeem Hasan

Preprint number: UUITP-27/22

It is well-known that six-dimensional superconformal field theories can be exploited to unravel interesting features of lower-dimensional theories obtained via compactifications. In this short note we discuss a new application of 6d (2,0) theories in constructing 4d theories with Kramers-Wannier-like non-invertible symmetries. Our methods allow to recover previously known results, as well as to exhibit infinitely many new examples of four dimensional theories with "M-ality" 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.

Authors: Ulf Danielsson, Vincent Van Hemelryck and Thomas Van Riet

Preprint Number: UUITP-26/22

Abstract: We demonstrate that, if the usual phenomenological compactifications of IIB string theory with warped throats and anti-branes make sense, there must exist spherical brane shells in 4d that are overcharged. They correspond to classical over-extremal objects but without the usual naked singularities. The objects are made from D3 particles that puff into spherical 5-branes that stabilise at finite radii in 4d and whose inside corresponds to the supersymmetric AdS vacuum. One can think of these shells as stabilised Brown-Teitelboim bubbles. We find that these objects can be significantly larger than the string scale depending on the details of the warped compactification.

Authors: Magdalena Larfors, Andre Lukas, Fabian Ruehle, Robin Schneider

Preprint number: UUITP-25/22

We introduce neural networks to compute numerical Ricci-flat CY metrics for complete intersection and Kreuzer-Skarke Calabi-Yau 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 point-sampling 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 bi-cubic manifold and a Kreuzer-Skarke manifold with Picard number two. We show that volumes and line bundle slopes can be reliably computed from the resulting Ricci-flat metrics. We also apply our results to compute an approximate Hermitian-Yang-Mills connection on a specific line bundle on the bi-cubic.

Authors: Rafael Aoude, Kays Haddad, Andreas Helset

Preprint number: UUITP-24/22

Making use of the recently-derived, all-spin, opposite-helicity 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 even-in-spin 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 aligned-spin scattering.

Authors: Da Liu, Zhewei Yin

Preprint number: UUITP-23/22

We study the three-particle and four-particle scattering amplitudes for an arbitrary, finite number of massive scalars, spinors and vectors by employing the on-shell massive spinor formalism. We consider the most general three-particle 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 N-particle scattering amplitudes at tree-level should grow at most as O(E^(4-N)) in the high energy hard scattering limit, i.e. at fixed non-zero angles. Then the factorizable parts of the four-particle amplitudes are calculated by gluing the on-shell three-particle amplitudes together and utilizing the fact that tree-level amplitudes have only simple poles. The contact parts of the four-particle amplitudes are further determined by tree unitarity, which also puts strong constraints on the possible allowed three-particle 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 on-shell understanding of spontaneously broken gauge theories.

Authors: Michele Del Zotto and Iñaki García Etxebarria

Preprint number: UUITP-22/22

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 Coulomb-like 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.

Authors: Tim Adamo, John Joseph M. Carrasco, Mariana Carrillo-González, Marco Chiodaroli, Henriette Elvang, Henrik Johansson, Donal O'Connell, Radu Roiban, Oliver Schlotterer

Preprint number: UUITP-21/22

The double-copy 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 double-copy, its applications, current research and future challenges.

Authors: Paolo Di Vecchia, Carlo Heissenberg, Rodolfo Russo, Gabriele Veneziano

Preprint: UUITP-20/22

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 post-Minkowskian (PM) expansion whose validity extends from the non-relativistic to the most extreme ultra-relativistic (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 soft-radiation 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 non-analyticity 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.

Authors: Francesco Alessio, Paolo Di Vecchia

Preprint: UUITP-19/22

Abstract: Starting from the leading soft term of the 5-point 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 two-loop
eikonal. Then, using analyticity and crossing symmetry, we determine the
radiative contribution to the real part of the two-loop 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.

Authors: Zvi Bern, John Joseph Carrasco, Marco Chiodaroli, Henrik Johansson, Radu Roiban

Preprint: UUITP-18/22

Advances in scattering amplitudes have exposed previously-hidden color-kinematics and double-copy structures in theories ranging from gauge and gravity theories to effective field theories such as chiral perturbation theory and the Born-Infeld model. These novel structures both simplify higher-order calculations and pose tantalizing questions related to a unified framework underlying relativistic quantum theories. This introductory mini-review article invites further exploration of these topics. After a brief introduction to color-kinematics duality and the double copy as they emerges at tree and loop-level in gauge and gravity theories, we present two distinct examples: 1) an introduction to the web of double-copy-constructible theories, and 2) a discussion on the application of the double copy to calculation relevant to gravitational-wave physics.

Authors: Michele Del Zotto, Iñaki García Etxebarria, Sakura Schäfer-Nameki

Preprint: UUITP-17/22

Quantum Field Theories engineered in M-theory can have 2-group symmetries, mixing 0-form and 1-form symmetry backgrounds in non-trivial ways. In this paper we develop methods for determining the 2-group structure from the boundary geometry of the M-theory background. We illustrate these methods in the case of 5d theories arising from M-theory on ordinary and generalised toric Calabi-Yau cones, including cases in which the resulting theory is non-Lagrangian. Our results confirm and elucidate previous results on 2-groups from geometric engineering.

Authors: Paolo Di Vecchia, Carlo Heissenberg, Rodolfo Russo

Preprint: UUITP-16/22

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 zero-frequency 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.

Authors: Luca Griguolo, Rodolfo Panerai, Jacopo Papalini, Domenico Seminara

Preprint: UUITP-15/22

TT-deformed two-dimensional 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 well-defined 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 positive-energy 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 instanton-like subtractions. For each flux sector, we show that the semiclassical contribution is dominated by the deformed classical action. The theory is observed to undergo infinite-order phase transitions for certain values of μ, associated with the vanishing of Polyakov-loop correlators.

Authors: André Kaderli and Carlos Rodriguez

Preprint number: UUITP-14/22

We study integrals appearing in intermediate steps of one-loop open-string 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 Knizhnik-Zamolodchikov-Bernard (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 so-called universal case is written in terms of the genus-one Drinfeld-Kohno 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.

Authors: Nathan Berkovits, Eric D'Hoker, Michael B. Green, Henrik Johansson, Oliver Schlotterer

Preprint number: UUITP-13/22

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.

Authors: Rafael Aoude, Kays Haddad, Andreas Helset

Preprint number: UUITP-12/22

Abstract: The classical scattering of spinning objects is well described by the spinor-helicity formalism for heavy particles. Using these variables, we derive spurious-pole-free, opposite-helicity Compton amplitudes (factorizing on physical poles to the minimal, all-spin three-point 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 structures---motivated by lower spin multipoles of black hole scattering---at the second post-Minkowskian (2PM) order. For QED and gravity, this leaves a modest number of unfixed coefficients parametrizing contact-term deformations, while the QCD amplitude is uniquely determined. Our gravitational Compton amplitude allows us to push the state-of-the-art of spinning-2PM 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 higher-spin parts of the 2PM amplitude.

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: UUITP-11/22

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 self-energy 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 Yang-Mills 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.

Authors: Ulf Lindström

Preprint number: UUITP-10/22

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.

Authors: Victor Alekseev, Guido Festuccia, Victor Mishnyakov, Nicolai Terziev and Maxim Zabzine

Preprint number: UUITP-09/22

We present a systematic study of ${\cal N}=(2,2)$ supersymmetric non-linear 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 self-duality 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 non-dynamical supersymmetric background gauge multiplet. We discuss the localization locus and perform a one-loop calculation around the constant maps. We argue that the theory can be reduced to some exotic model over the moduli space of holomorphic disks.

Authors: Marco Chiodaroli, Murat Günaydin, Henrik Johansson and Radu Roiban

Preprint Number: UUITP-08/22

Five-dimensional 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 six-dimensional tensor theories. Five-dimensional 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 five-dimensional version of the spinor-helicity formalism, applicable to massless, massive and supersymmetric states. We give explicit representations for on-shell spinor and polarization variables such that the little-group symmetry and gauge redundancy are manifest. Massive self-dual tensor states are discussed in some detail, as well as all the on-shell supermultiplets that can appear in matter-coupled gauge and supergravity theories. As a byproduct of considering supersymmetry in the presence of central charge, we obtain massless ten-dimensional Majorana-Weyl spinors as products of five-dimensional massive spinors.

Authors: Ulf Lindström and Özgür Sarıoğlu

Preprint Number: UUITP-07/22

In this contribution we have collected some facts about Killing and Killing-Yano 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.

 

Authors: Ulf Lindström and Özgür Sarıoğlu

Preprint Number: UUITP-06/22

We construct invariants for bosonic and spinning tensionless (null) strings in back- grounds that carry Killing or Killing-Yano 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 Kerr-Newman background.

Authors: Alex Edison, Michèle Levi

Preprint Number: UUITP-05/22

We introduce a novel framework to study high-order gravitational effects on a binary from the scattering of its emitted gravitational radiation. Here we focus on the radiation-reaction due to the background of the binary’s gravitational potential, namely on the so-called tail effects. We start from the effective field theory of a binary composite particle, and through multi-loop 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 radiation-reaction effect – at the four-loop level and the seventh order in post-Newtonian gravity – shedding new light on the higher-order effects, and completing the state of the art.

Authors: Franziska Porkert, Oliver Schlotterer

Preprint number: UUITP-04/22

We present a method to compute the integrands of one-loop Einstein-Yang-Mills amplitudes for any number of external gauge and gravity multiplets. Our construction relies on the double-copy structure of Einstein-Yang-Mills as (super-)Yang-Mills with the so-called YM+phi^3 theory -- pure Yang-Mills coupled to bi-adjoint scalars -- which we implement via one-loop Cachazo-He-Yuan formulae. The YM+phi^3 building blocks are obtained from forward limits of tree-level 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 dimension-agnostic relations that reduce loop integrands of Einstein-Yang-Mills to those of pure gauge theories. On the other hand, we present four-point results for maximal and half-maximal supersymmetry where all supersymmetry cancellations are exposed. In the half-maximal case, we determine six-dimensional anomalies due to chiral hypermultiplets in the loop.