Preprints 2021

Poincaré series for modular graph forms at depth two II. Iterated integrals of cusp forms
Authors: Daniele Dorigoni, Axel Kleinschmidt and Oliver Schlotterer
Preprint number: UUITP42/21
Abstract: We continue the analysis of modular invariant functions, subject to inhomogeneous Laplace eigenvalue equations, that were determined in terms of Poincaré series in a companion paper. The source term of the Laplace equation is a product of (derivatives of) two nonholomorphic Eisenstein series whence the modular invariants are assigned depth two. These modular invariant functions can sometimes be expressed in terms of singlevalued iterated integrals of holomorphic Eisenstein series as they appear in generating series of modular graph forms. We show that the set of iterated integrals of Eisenstein series has to be extended to include also iterated integrals of holomorphic cusp forms to find expressions for all modular invariant functions of depth two. The coefficients of these cusp forms are identified as ratios of their Lvalues inside and outside the critical strip.

Poincaré series for modular graph forms at depth two I: Seeds and Laplace systems
Authors: Daniele Dorigoni, Axel Kleinschmidt and Oliver Schlotterer
Preprint number: UUITP41/21
Abstract: We derive new Poincaréseries representations for infinite families of nonholomorphic modular invariant functions that include modular graph forms as they appear in the lowenergy expansion of closedstring scattering amplitudes at genus one. The Poincaré series are constructed from iterated integrals over single holomorphic Eisenstein series and their complex conjugates, decorated by suitable combinations of zeta values. We evaluate the Poincaré sums over these iterated Eisenstein integrals of depth one and deduce new representations for all modular graph forms built from iterated Eisenstein integrals at depth two. In a companion paper, some of the Poincaré sums over depthone integrals going beyond modular graph forms will be described in terms of iterated integrals over holomorphic cusp forms and their Lvalues.

Evidence for an Algebra of G2 Instantons
Authors: Michele Del Zotto, Jihwan Oh, Yehao Zhou
Preprint number: UUITP40/21
Abstract: In this short note, we present some evidence towards the existence of an algebra of BPS G_{2} instantons. These are instantonic configurations that govern the partition functions of 7d SYM theories on local G_{2} holonomy manifolds X. To shed light on such structure, we begin investigating the relation with parent 4d N=1 theories obtained by geometric engineering Mtheory on X. The main point of this paper is to substantiate the following dream: the holomorphic sector of such theories on multicentered TaubNUT spaces gives rise to an algebra whose characters organise the G_{2} instanton partition function. As a first step towards this program, we argue by string duality that a multitude of geometries X exist that are dual to wellknown 4d SCFTs arising from D3 branes probes of CY cones: all these models are amenable to analysis along the lines suggested by Dijkgraaf, Gukov, Neitzke and Vafa in the context of topological Mtheory. Moreover, we discuss an interesting relation to Costello's twisted Mtheory, which arises at local patches, and is a key ingredient in identifying the relevant algebras.

The Characteristic Dimension of Fourdimensional N=2 SCFTs
Authors: Sergio Cecotti, Michele Del Zotto, Mario Martone, and Robert Moscrop
Preprint: UUITP39/21
In this paper we introduce the characteristic dimension of a four dimensional N=2 superconformal field theory, which is an extraordinary simple invariant determined by the scaling dimensions of its Coulomb branch operators. We prove that only nine values of the characteristic dimension are allowed, −∞, 1 ,6/5, 4/3, 3/2, 2, 3, 4, and 6, thus giving a new organizing principle to the vast landscape of 4d N=2 SCFTs. Whenever the characteristic dimension differs from 1 or 2, only very constrained special Kähler geometries (i.e. isotrivial, diagonal and rigid) are compatible with the corresponding set of Coulomb branch dimensions and extremely special, maximally strongly coupled, BPS spectra are allowed for the theories which realize them. Our discussion applies to superconformal field theories of arbitrary rank, i.e. with Coulomb branches of any complex dimension. Along the way, we predict the existence of new N=3 theories of rank two with nontrivial oneform symmetries.

GreenSchwarz and Pure Spinor Formulations of Chiral Strings
Author: Max Guillen
Preprint number: UUITP38/21
Bosonic and RNS chiral strings have been defined from a singular gauge fixing of the respective Polyakov and spinning string actions, enforcing, among other things, the finite nature of their physical spectra. Except for the heterotic case, the tensionless limits of such chiral models have been shown to describe the same field theories predicted by their ambitwistor analogues. In this paper, we study the GreenSchwarz formulation for Type II and heterotic superstrings in a singular gauge. After performing a lightcone gauge analysis, their physical spectra are shown to match those of RNS chiral strings, and their respective tensionless limits are found to describe the same field theories predicted by RNS ambitwistor strings. Their pure spinor counterparts are then introduced by making use of the OdaTonin method. In doing so, symmetries hidden in the pure spinor ambitwistor string action become manifest, proposals motivating the sectorized pure spinor BRST charges find simple grounds, and integrated vertex operators emerge naturally.

10D SuperYangMills Scattering Amplitudes From Its Pure Spinor Action
Authors: Maor BenShahar and Max Guillen
Preprint number: UUITP37/21
Using the pure spinor master action for 10D superYangMills in the gauge $b_{0}V = Q\Xi$, treelevel scattering amplitudes are calculated through the perturbiner method, and shown to match those obtained from pure spinor CFT techniques. We find kinematic numerators made of nested $b$ghost operators, and show that the Siegel gauge condition $b_{0}V = 0$ gives rise to colorkinematics duality satisfying numerators whose Jacobi identity follows from that of a kinematic algebra.

Deep multitask mining CalabiYau fourfolds
Authors: Harold Erbin, Riccardo Finotello, Robin Schneider and Mohamed Tamaazousti
Preprint number: UUITP36/21
Abstract: We continue earlier efforts in computing the dimensions of tangent space cohomologies of CalabiYau manifolds using deep learning. In this paper, we consider the dataset of all CalabiYau fourfolds constructed as complete intersections in products of projective spaces. Employing neural networks inspired by stateoftheart computer vision architectures, we improve earlier benchmarks and demonstrate that all four nontrivial Hodge numbers can be learned at the same time using a multitask architecture. With 30% (80%) training ratio, we reach an accuracy of 100% for $h^{(1,1)}$ and 97% for $h^{(2,1)}$ (100% for both), 81% (96%) for $h^{(3,1)}$, and 49% (83%) for $h^{(2,2)}$. Assuming that the Euler number is known (since it is easy to compute) and taking into account the linear constraint arising from index computations, we get 100% total accuracy.

Twoloop superstring fivepoint amplitudes III, construction via the RNS formulation: even spin structures
Authors: Eric D'Hoker and Oliver Schlotterer
Preprint number: UUITP35/21
Abstract: The contribution from even spin structures to the genustwo amplitude for five massless external NS states in Type II and Heterotic superstrings is evaluated from first principles in the RNS formulation. Using chiral splitting with the help of loop momenta this problem reduces to the evaluation of the corresponding chiral amplitude, which is carried out using the same techniques that were used for the genustwo amplitude with four external NS states. The results agree with the parityeven NS components of a construction using chiral splitting and pure spinors given in earlier companion papers arXiv:2006.05270 and arXiv:2008.08687.

Compton BlackHole Scattering for s ≤ 5/2
Authors: Marco Chiodaroli, Henrik Johansson and Paolo Pichini
Preprint number: UUITP34/21
Abstract: Quantum scattering amplitudes for massive matter have received new attention in connection to classical calculations relevant to gravitationalwave physics. Amplitude methods and insights are now employed for precision computations of observables needed for describing the gravitational dynamics of bound massive objects such as black holes. An important direction is the inclusion of spin effects needed to accurately describe rotating (Kerr) black holes. Higherspin amplitudes introduced by ArkaniHamed, Huang and Huang at three points have by now a firm connection to the effective description of Kerr blackhole physics. The corresponding Compton higherspin amplitudes remain however an elusive open problem. Here we draw from results of the higherspin literature and show that physical insights can be used to uniquely fix the Compton amplitudes up to spin 5/2, by imposing a constraint on a threepoint higherspin current that is a necessary condition for the existence of an underlying unitary theory. We give the unique effective Lagrangians up to spin 5/2, and show that they reproduce the previouslyknown amplitudes. For the multigraviton amplitudes analogous to the Compton amplitude, no further corrections to our Lagrangians are expected, and hence such amplitudes are uniquely predicted. As an essential tool, we introduce a modified version of the massive spinorhelicity formalism which allows us to conveniently obtain higherspin states, propagators and compact expressions for the amplitudes

Two applications of the analytic conformal bootstrap: A quick tour guide
Authors: Agnese Bissi, Parijat Dey and Giulia Fardelli
Preprint number: UUITP33/21
Abstract: We review the recent developments in the study of conformal field theories in generic space time dimensions using the methods of the conformal bootstrap, in its analytic aspect. These techniques are based solely on symmetries, in particular in the analytic structure and in the associativity of the operator product expansion. We focus on two applications of the analytic conformal bootstrap: the study of the $\epsilon$ expansion of the Wilson Fisher model via the introduction of a dispersion relation and the large $N$ expansion of maximally supersymmetric Super Yang Mills theory in four dimensions.

On refined ChernSimons and refined ABJ matrix models
Authors: Luca Cassia and Maxim Zabzine
Preprint number: UUITP32/21
Abstract: We consider the matrix model of U(N) refined ChernSimons theory on S³ for the unknot. We derive a qdifference operator whose insertion in the matrix integral reproduces an infinite set of Ward identities which we interpret as qVirasoro constraints. The constraints are rewritten as difference equations for the generating function of Wilson loop expectation values which we solve as a recursion for the correlators of the model. The solution is repackaged in the form of superintegrability formulas for Macdonald polynomials. Additionally, we derive an equivalent qdifference operator for a similar refinement of ABJ theory and show that the corresponding qVirasoro constraints are equal to those of refined ChernSimons for a gauge supergroup U(NM). Our equations and solutions are manifestly symmetric under Langlands duality q ↔ 1/t which correctly reproduces 3d Seiberg duality when q is a specific root of unity.

Oneloop matrix elements of effective superstring interactions: alpha'expanding loop integrands
Authors: Alex Edison, Max Guillen, Henrik Johansson, Oliver Schlotterer and Fei Teng
Preprint number: UUITP31/21
Abstract: In the lowenergy effective action of string theories, nonabelian gauge interactions and supergravity are augmented by infinite towers of highermassdimension operators. We propose a new method to construct oneloop matrix elements with insertions of operators D^{2k} F^n and D^{2k} R^n in the treelevel effective action of typeI and typeII superstrings. Inspired by ambitwistor string theories, our method is based on forward limits of modulispace integrals using string treelevel amplitudes with two extra points, expanded in powers of the inverse string tension alpha'. Similar to oneloop ambitwistor computations, intermediate steps feature nonstandard linearized Feynman propagators which eventually recombine to conventional quadratic propagators. With linearized propagators the loop integrand of the matrix elements obey oneloop versions of the monodromy and KLT relations. We express a variety of four and fivepoint examples in terms of quadratic propagators and formulate a criterion on the underlying genusone correlation functions that should make this recombination possible at all orders in alpha'. The ultraviolet divergences of the oneloop matrix elements are crosschecked against the nonseparating degeneration of genusone integrals in string amplitudes. Conversely, our results can be used as a constructive method to determine degenerations of elliptic multiple zeta values and modular graph forms at arbitrary weight.

Squashing and supersymmetry enhancement in three dimensions
Authors: Joseph Minahan, Usman Naseer and Charles Thull
Preprint number: UUITP30/21
We consider massdeformed theories with ${\cal N}\geq2$ supersymmetry on round and squashed threespheres. By embedding the supersymmetric backgrounds in extended supergravity we show that at special values of mass deformations the supersymmetry is enhanced on the squashed spheres. When the $3d$ partition function can be obtained by a limit of a $4d$ index we also show that for these special mass deformations only the states annihilated by extra supercharges contribute to the index. By using an equivalence between partition functions on squashed spheres and ellipsoids, we explain the recently observed squashing independence of the partition function of massdeformed ABJM theory on the ellipsoid. We provide further examples of such simplification for various $3d$ supersymmetric theories.

Scaleseparated AdS$_4$ vacua of IIA orientifolds and Mtheory
Authors: N. Cribiori, D. Junghans, V. Van Hemelryck, T. Van Riet, T. Wrase
Preprint number: UUITP29/21
Abstract: We revisit various aspects of AdS$_4$ flux vacua with scale separation in type II supergravity and Mtheory. We show that massless IIA allows both weakly and strongly coupled solutions for which the classical orientifold backreaction can be tuned small. This is explicitly verified by computing the backreaction at leading order in perturbation theory. We give evidence that the strongly coupled solutions can be lifted to scaleseparated and sourceless (but classically singular) geometries in 11D supergravity.

Gauged 2form Symmetries in 6D SCFTs Coupled to Gravity
Authors: Andreas P. Braun, PaulKonstantin Oehlmann, and Magdalena Larfors
Preprint number: UUITP28/21
Abstract: We study six dimensional supergravity theories with superconformal sectors(SCFTs). Instances of such theories can be engineered using type IIB strings, or more generally FTheory, which translates field theoretic constraints to geometry. Specifically, we study the fate of the discrete 2form global symmetries of the SCFT sectors. For both $(2,0)$ and $(1,0)$ theories we show that whenever the charge lattice of the SCFT sectors is nonprimitively embedded into the charge lattice of the supergravity theory, there is a subgroup of these 2form symmetries that remains unbroken by BPS strings. By the absence of global symmetries in quantum gravity, this subgroup much be gauged. Using the embedding of the charge lattices also allows us to determine how the gauged 2form symmetry embeds into the 2form global symmetries of the SCFT sectors, and we present several concrete examples, as well as some general observations. As an alternative derivation, we recover our results for a large class of models from a dual perspective upon reduction to five dimensions.

Bulk reconstruction and Bogoliubov transformations in AdS$_2$
Authors: Parijat Dey and Nirmalya Kajuri
Preprint number: UUITP27/21
Abstract: In the bulk reconstruction program, one constructs boundary representations of bulk fields. However, the boundary representations derived in global and AdSRindler coordinates appear to be inequivalent as the AdSRindler smearing function is known to diverge in dimensions greater than two. This is an apparent paradox. We investigate the relation between the two representations for AdS$_2$. We obtain the AdSRindler smearing function for massive and massless fields and show that the global and AdSRindler boundary representations are related by conformal transformations. We also use the boundary representations of creation and annihilation operators to compute the Bogoliubov transformation relating global modes to AdSRindler modes for both massive and massless particles.

The FL bound and its phenomenological implications
Authors: Miguel Montero, Cumrun Vafa, Thomas Van Riet and Gerben Venken
Preprint number: UUITP26/21
Abstract: Demanding that charged Nariai black holes in (quasi)de Sitter space decay
without becoming superextremal implies a lower bound on the masses of charged particles, known as the Festina Lente (FL) bound. In this paper we elucidate various aspects of this bound as well as extensions of it to d > 4 and to situations with scalar potentials and dilatonic couplings. We also discuss phenomenological implications of FL including an explanation of why the Higgs potential cannot have a local minimum at the origin, thus explaining why the weak force must be broken. For constructions of metastable dS involving antibrane uplift scenarios, even though the throat region is consistent with FL, the bound implies that we cannot have any light charged matter elds coming from any far away region in the compactified geometry, contrary to the fact that they are typically expected to arise in these scenarios. This strongly suggests that introduction of warped antibranes in the throat cannot be decoupled from the bulk dynamics as is commonly assumed. Finally, we provide some evidence that in certain situations the FL bound can have implications even with gravity decoupled and illustrate this in the context of noncompact throats. 
Nonperturbative effects and resurgence in JT gravity at finite cutoff
Authors: Luca Griguolo, Rodolfo Panerai, Jacopo Papalini, Domenico Seminara
Preprint number: UUITP25/21
Abstract: We investigate the nonperturbative structure of JackiwTeitelboim gravity at finite cutoff, as given by its proposed formulation in terms of a TTdeformed Schwarzian quantum mechanics. Our starting point is a careful computation of the disk partition function to all orders in the perturbative expansion in the cutoff parameter. We show that the perturbative series is asymptotic and that it admits a precise completion exploiting the analytical properties of its Borel transform, as prescribed by resurgence theory. The final result is then naturally interpreted in terms of the nonperturbative branch of the TTdeformed spectrum. The finitecutoff trumpet partition function is computed by applying the same strategy. In the second part of the paper, we propose an extension of this formalism to arbitrary topologies, using the basic gluing rules of the undeformed case. The WeilPetersson integrations can be safely performed due to the nonperturbative corrections and give results that are compatible with the flow equation associated with the TT deformation. We derive exact expressions for general topologies and show that these are captured by a suitable deformation of the EynardOrantin topological recursion. Finally, we study the "slope" and "ramp" regimes of the spectral form factor as functions of the cutoff parameter.

On the squashed sevensphere operator spectrum
Authors: S. Ekhammar, B. E. W. Nilsson
Preprint number: UUITP24/21
Abstract: We derive major parts of the eigenvalue spectrum of the operators on the squashed sevensphere that appear in the compactification of elevendimensional supergravity. These spectra determine the mass spectrum of the fields in AdS_{4} and are important for the corresponding N =1 supermultiplet structure. This work is a continuation of the work in [1] where the complete spectrum of irreducible isometry representations of the fields in AdS_{4} was derived for this compactification. Some comments are also made concerning the G_{2} holonomy and its implications on the structure of the operator equations on the squashed sevensphere.

Infrared Divergences and the Eikonal
Authors: Carlo Heissenberg
Preprint number: UUITP23/21
Abstract: The aim of this note is to explore the interplay between the eikonal resummation in impactparameter space and the exponentiation of infrared divergences in momentum space for gravity amplitudes describing collisions of massive objects. The eikonal governs the classical dynamics relevant to the twobody problem, and its infrared properties are directly linked to the zero frequency limit of the gravitational wave emission spectrum and to radiation reaction effects. Combining eikonal and infrared exponentiations it is possible to derive these properties at a given loop order starting from lowerloop data. This is illustrated explicitly in N = 8 supergravity and in general relativity by deriving the divergent part of the twoloop eikonal from treelevel and oneloop elastic amplitudes.

A higherdimensional view on quantum cosmology
Authors: U. H. Danielsson, D. Panizo, R. Tielemans, T. Van Riet
Preprint number: UUITP22/21
Abstract: We argue that the choice of boundary condition for the wavefunction in quantum cosmology depends on the UV completion of general relativity. We provide an explicit example using a braneworld scenario in which a de Sitter cosmology is induced on the surface of a CDL bubble in a 5dimensional AdS space. The corresponding boundary conditions are unambigously fixed by demanding consistency with the known physics of bubble nucleation and this selects the Vilenkin choice from a 4D viewpoint.

NexttoMHV YangMills kinematic algebra
Authors: Gang Chen, Henrik Johansson, Fei Teng and Tianheng Wang
Preprint number: UUITP21/21
Abstract: Kinematic numerators of YangMills scattering amplitudes possess a rich Lie algebraic structure that suggest the existence of a hidden infinitedimensional kinematic algebra. Explicitly realizing such a kinematic algebra is a longstanding open problem that only has had partial success for simple helicity sectors. In past work, we introduced a framework using tensor currents and fusion rules to generate BCJ numerators of a special subsector of NMHV amplitudes in YangMills theory. Here we enlarge the scope and explicitly realize a kinematic algebra for all NMHV amplitudes. Master numerators are obtained directly from the algebraic rules and through commutators and kinematic Jacobi identities other numerators can be generated. Inspecting the output of the algebra, we conjecture a closedform expression for the master BCJ numerator up to any multiplicity. We also introduce a new method, based on group algebra of the permutation group, to solve for the generalized gauge freedom of BCJ numerators. It uses the recently introduced binary BCJ relations to provide a complete set of NMHV kinematic numerators that consist of pure gauge.

New currents with KillingYano tensors
Authors: Ulf Lindström and Özgür Sarioglu
Preprint number: UUITP20/21
Abstract: New relations involving the Riemann, Ricci and Einstein tensors that have to hold for a given geometry to admit KillingYano tensors are described. These relations are then used to introduce novel conserved currents involving such KillingYano tensors. For a particular current based on the Einstein tensor, we discuss the issue of conserved charges and consider implications for the matter coupling to gravity. The condition on the background geometry to allow asymptotic conserved charges for a current introduced by Kastor and Traschen is found and a number of other new aspects of this current are commented on.

Bethe Algebra using Pure Spinors
Authors: Simon Ekhammar, Dmytro Volin
Preprint number: UUITP19/21
Abstract: We propose a gl(r)covariant parameterisation of Bethe algebra appearing in so(2r) integrable models, demonstrate its geometric origin from a fused flag, and use it to compute the spectrum of periodic rational spin chains, for various choices of the rank r and Drinfeld polynomials.

The Eikonal Approach to Gravitational Scattering and Radiation at O(G^3)
Authors: Paolo di Vecchia, Carlo Heissenberg, Rodolfo Russo, Gabriele Veneziano
Preprint number: UUITP18/21
Abstract: Using N=8 supergravity as a theoretical laboratory, we extract the 3PM gravitational eikonal for two colliding massive scalars from the classical limit of the corresponding elastic twoloop amplitude. We employ the eikonal phase to obtain the physical deflection angle and to show how its nonrelativistic (NR) and ultrarelativistic (UR) regimes are smoothly connected. Such a smooth interpolation rests on keeping contributions to the loop integrals originating from the full soft region, rather than restricting it to its potential subregion. This task is efficiently carried out by using the method of differential equations with complete nearstatic boundary conditions. In contrast to the potentialregion result, the physical deflection angle includes radiationreaction contributions that are essential for recovering the finite and universal UR limit implied by general analyticity and crossing arguments. We finally discuss the real emission of massless states, which accounts for the imaginary part of the 3PM eikonal and for the dissipation of energymomentum. Adopting a direct approach based on unitarity and on the classical limit of the inelastic treelevel amplitude, we are able to treat N=8 and General Relativity on the same footing, and to complete the conservative 3PM eikonal in Einstein's gravity by the addition of the radiationreaction contribution. We also show how this approach can be used to compute waveforms, as well as the differential and integrated spectra, for the different radiated massless fields.

Scattering Massive String Resonances through FieldTheory Methods
Authors: Max Guillen, Henrik Johansson, Renann Lipinski Jusinskas, Oliver Schlotterer
Preprint number: UUITP17/21
Abstract: We present a new method, exact in alpha', to explicitly compute string treelevel amplitudes involving one massive state and any number of massless ones. This construction relies on the socalled twisted heterotic string, which admits only gauge multiplets, a gravitational multiplet, and a single massive supermultiplet in its spectrum. In this simplified model, we determine the modulispace integrand of all amplitudes with one massive state using BerendsGiele currents of the gauge multiplet. These integrands are then straightforwardly mapped to gravitational amplitudes in the twisted heterotic string and to the corresponding massive amplitudes of the conventional typeI and typeII superstrings.

Monodromy Defects in Free Field Theories
Authors: Lorenzo Bianchi, Adam Chalabi, Vladimír Procházka, Brandon Robinson, and
Jacopo SistiPreprint number: UUITP 16/21
Abstract: We study codimension two monodromy defects in theories of conformally
coupled scalars and free Dirac fermions in arbitrary d dimensions. We characterise this
family of conformal defects by computing the onepoint functions of the stresstensor and
conserved current for Abelian flavour symmetries as well as twopoint functions of the
displacement operator. In the case of d = 4, the normalisation of these correlation functions
are related to defect Weyl anomaly coefficients, and thus provide crucial information about
the defect conformal field theory. We provide explicit checks on the values of the defect
central charges by calculating the universal part of the defect contribution to entanglement
entropy. Moreover, we leverage the nonsupersymmetric free field results to compute a
novel defect Weyl anomaly coefficient in a d = 4 theory of free N = 2 hypermultiplets.
In carefully studying the defect operator product expansion, we identify notable relevant
operators in the defect theories and use them to study the behaviour of the defect under
renormalisation group flow. 
Curing with hemlock: escaping the swampland using instabilities from string theory
Authors: Souvik Banerjee, Ulf Danielsson, Suvendu Giri
Preprint number: UUITP15/21
Abstract: In this essay we will take a wonderful ride on a dark bubble with strings attached, which carries our universe out of the swampland and makes it realizable in the landscape of string theory. To find the way to the landscape, we make use of apparently hostile corners of the swampland and their instabilities.

Kinematic numerators from the worldsheet: cubic trees from labelled trees
Authors: Linghui Hou, Song He, Jintian Tian and Yong Zhang
Preprint number: UUITP14/21
Abstract: In this note we revisit the problem of explicitly computing treelevel scattering amplitudes in various theories in any dimension from worldsheet formulas. The latter are known to produce cubic tree expansion of tree amplitudes with kinematic numerators automatically satisfying Jacobi identities, once any halfintegrand on the worldsheet is reduced to logarithmic functions. We review a natural class of worldsheet functions called “Cayley functions”, which are in onetoone correspondence with labelled trees, and natural expansions of known halfintegrands onto them with coefficients that are particularly compact building blocks of kinematic numerators. We present a general formula expressing the kinematic numerator of any cubic tree as a linear combination of these coefficients of labelled trees, including the usual combination in terms of master numerators as a special case. Our results provide an efficient algorithm, which is implemented in a Mathematica package, for computing tree amplitudes in nonlinear sigma models, special Galileon,YangMillsscalar, EinsteinYangMills, DiracBornInfeld and so on.

Generalized Vanishing Theorems for Yukawa Couplings in Heterotic Compactifications
Authors: Lara B. Anderson, James Gray, Magdalena Larfors, Matthew Magill, Robin Schneider
Preprint number: UUITP13/21
Abstract: Heterotic compactifications on CalabiYau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be topological in nature. Recent results in the literature used differential geometric methods to explain the origin of some of this structure. A vanishing theorem was given which showed that the effect could be attributed, in part, to the embedding of the CalabiYau manifolds of interest inside higher dimensional ambient spaces, if the gauge bundles involved descended from vector bundles on those larger manifolds. In this paper, we utilize an algebrogeometric approach to provide an alternative derivation of some of these results, and are thus able to generalize them to a much wider arena than has been considered before. For example, we consider cases where the vector bundles of interest do not descend from bundles on the ambient space. In such a manner we are able to highlight the ubiquity with which textures of vanishing Yukawa couplings can be expected to arise in heterotic compactifications, with multiple different constraints arising from a plethora of different geometric features associated to the gauge bundle.

Playing with the index of Mtheory
Authors: Michele del Zotto, Nikita Nekrasov, Nicolo Piazzalunga, Maxim Zabzine
Preprint number: UUITP12/21
Abstract: Motivated by Mtheory, we study rank n Ktheoretic DonaldsonThomas theory on a toric threefold X. In the presence of compact fourcycles, we discuss how to include the contribution of D4branes wrapping them. Combining this with a simple assumption on the (in)dependence on Coulomb moduli in the 7d theory, we show that the partition function factorizes and, when X is CalabiYau and it admits an ADE ruling, it reproduces the 5d master formula for the geometrically engineered theory on A(n1) ALE space, thus extending the usual geometric engineering dictionary to n>1. We finally speculate about implications for instanton counting on TaubNUT.

Nonflat elliptic fourfolds, threeform cohomology and strongly coupled theories in four dimensions
Authors: PaulKonstantin Oehlmann
Preprint number: UUITP11/21
Abstract: In this note we consider smooth elliptic CalabiYau fourfolds whose fiber ceases to be flat over compact Riemann surfaces of genus g in the base. These nonflat fibers contribute Kähler moduli to the fourfold but also add to the threeform cohomology for g>0. In F/Mtheory these sectors are to be interpreted as compactifications of six/five dimensional N=(1,0) superconformal matter theories. The threeform cohomology leads to additional chiral singlets proportional to the dimension of five dimensional Coulomb branch of those sectors. We construct explicit examples for Estring theories as well as higher rank cases. For the Estring theories we further investigate conifold transitions that remove those nonflat fibers. First, we show how nonflat fibers can be deformed from curves down to isolated points in the base. This removes the chiral singlet of the threeforms and leads to nonperturbative fourpoint couplings among matter fields which can be understood as remnants of the former Estring. Alternatively, the nonflat fibers can be avoided by performing birational base changes, analogous to 6D tensor branches. For compact bases these transitions alternate all Hodge numbers but leave the Euler number invariant.

Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
Authors: Laurentiu Rodina, Zhewei Yin
Preprint number: UUITP10/21
Abstract: We generalize soft theorems of the nonlinear sigma model beyond the O(p^2) amplitudes and the coset of SU(N)×SU(N)/SU(N). We first discuss the flavor ordering of the amplitudes for the NambuGoldstone bosons of a general symmetry group representation, so that we can reinterpret the known O(p^2) single soft theorem for SU(N)×SU(N)/SU(N) in the context of a general group representation. We then investigate the special case of the fundamental representation of SO(N), where a special flavor ordering of the "pair basis" is available. We provide novel amplitude relations and a CachazoHeYuan formula for such a basis, and derive the corresponding single soft theorem. Next, we extend the single soft theorem for a general group representation to O(p^4), where for at least two specific choices of the O(p^4) operators, the leading nonvanishing pieces can be interpreted as new extended theory amplitudes involving biadjoint scalars, and the corresponding soft factors are the same as at O(p^2). Finally, we compute the general formula for the double soft theorem, valid to all derivative orders, where the leading part in the soft momenta is fixed by the O(p^2) Lagrangian, while any possible corrections to the subleading part are determined by the O(p^4) Lagrangian alone. Higher order terms in the derivative expansion do not contribute any new corrections to the double soft theorem.

Virasoro constraints revisited
Authors: Luca Cassia, Rebecca Lodin and Maxim Zabzine
Preprint number: UUITP09/21
Abstract: We revisit the Virasoro constraints and explore the relation to the Hirota bilinear equations. We furthermore investigate and provide the solution to nonhomogeneous Virasoro constraints, namely those coming from matrix models whose domain of integration has boundaries. In particular, we provide the example of Hermitean matrices with positive eigenvalues in which case one can find a solution by induction on the rank of the matrix model.

Coaction and doublecopy properties of configurationspace integrals at genus zero
Authors: Ruth Britto, Sebastian Mizera, Carlos Rodriguez, Oliver Schlotterer
Preprint number: UUITP08/21
Abstract: We investigate configurationspace integrals over punctured Riemann spheres from the viewpoint of the motivic Galois coaction and doublecopy structures generalizing the KawaiLewellenTye relations in string theory. For this purpose, explicit bases of twisted cycles and cocycles are worked out whose orthonormality simplifies the coaction. We present methods to efficiently perform and organize the expansions of configurationspace integrals in the inverse string tension alpha' or the dimensionalregularization parameter epsilon. Generatingfunction techniques open up a new perspective on the coaction of multiple polylogarithms in any number of variables and analytic continuations in the unintegrated punctures. We present a compact recursion for a generalized KLT kernel and discuss its origin from intersection numbers of Stasheff polytopes and its implications for correlation functions of twodimensional conformal field theories. We find a nontrivial example of correlation functions in (p,2) minimal models, which can be normalized to become uniformly transcendental in the p > \infty limit.

Fusion of conformal defects in four dimensions
Authors: Alexander Söderberg
Preprint number: UUITP07/21
Abstract: We consider two conformal defects close to each other in a free theory, and study what happens as the distance between them goes to zero. This limit is the same as zooming out, and the two defects have fused to another defect. As we zoom in we find a nonconformal effective action for the fused defect. Among other things this means that we cannot in general decompose the twopoint correlator of two defects in terms of other conformal defects. We prove the fusion using the path integral formalism by treating the defects as sources for a scalar in the bulk.

Almost contact structures on manifolds with a G2 structure
Authors: Xenia de la Ossa, Magdalena Larfors, Matthew Magill
Preprint number: UUITP06/21
Abstract: We review the construction of almost contact metric (three) structures on manifolds with a G2 structure. These are of interest for certain supersymmetric configurations in string and Mtheory. We compute the torsion of the SU(3) structure associated to an ACMS and apply these computations to heterotic G2 systems and supersymmetry enhancement. We initiate the study of the space of ACM3Ss, which is an infinite dimensional space with a local product structure and interesting topological features. Tantalising links between ACM3Ss and associative and coassociative submanifolds are observed.

Dark bubbles and black holes
Authors: Souvik Banerjee, Ulf Danielsson, Suvendu Giri
Preprint number: UUITP05/21
Abstract: In this paper we study shells of matter and black holes on the expanding bubbles realizing de Sitter space, that were proposed in arXiv:1807.01570. The explicit solutions that we find for the black holes, can also be used to construct RandallSundrum braneworld black holes in four dimensions.

Exploring SU(N) adjoint correlators in 3d
Authors: Andrea Manenti, Alessandro Vichi
Preprint number: UUITP04/21
Abstract: We use numerical bootstrap techniques to study correlation functions of scalars transforming in the adjoint representation of SU(N). We obtain upper bounds on operator dimensions for all the relevant representations and several values of $N$. We discover several families of kinks, which do not correspond to any known model and we discuss possible candidates. We then specialize to the case N=3,4, which has been conjectured to describe a phase transition respectively in the non compact complex projective space NCCP^2 and the antiferromagnetic complex projective model ACP^3. Lattice simulations provide strong evidence for the existence of a second order phase transition, while an effective field theory approach does not predict any fixed point. We identify a set of assumptions that constrain operator dimensions to a closed region overlapping with the lattice prediction.

Radiation Reaction from Soft Theorems
Authors: Paolo Di Vecchia, Carlo Heissenberg, Rodolfo Russo, Gabriele Veneziano
Preprint number: UUITP03/21
Abstract: Radiation reaction (RR) terms at the third postMinkowskian (3PM) order have recently been found to be instrumental in restoring smooth continuity between the nonrelativistic, relativistic, and ultrarelativistic (including the massless) regimes. Here we propose a new and intriguing connection between RR and soft (bremsstrahlung) theorems which shortcircuits the more involved conventional loop computations. Although first noticed in the context of the maximally supersymmetric theory, unitarity and analyticity arguments support the general validity of this 3PMorder connection that we apply, in particular, to Einstein's gravity and to its JordanBransDicke extension. In the former case we find full agreement with a recent result by Damour obtained through a very different reasoning.

Cosmic eggs to relax the cosmological constant
Authors: Thomas Hertog, Rob Tielemans, Thomas van Riet
Preprint number: UUITP02/21
Abstract: In theories with extra dimensions, the cosmological hierarchy problem can be thought of as the unnaturally large radius of the observable universe in KaluzaKlein units. We sketch a dynamical mechanism that relaxes this. In the early universe scenario we propose, three large spatial dimensions arise through tunneling from a 'cosmic egg', an effectively onedimensional configuration with all spatial dimensions compact and of comparable, small size. If the string landscape is dominated by lowdimensional compactifications, cosmic eggs would be natural initial conditions for cosmology. A quantum cosmological treatment of a toy model egg predicts that, in a variant of the HartleHawking state, cosmic eggs break to form higher dimensional universes with a small, but positive cosmological constant or quintessence energy. Hence cosmic egg cosmology yields a scenario in which the seemingly unnaturally small observed value of the vacuum energy can arise from natural initial conditions.

Inozemtsev system as SeibergWitten integrable system
Authors: Philip Argyres, Oleg Chalykh, Yongchao Lu
Preprint number: UUITP01/21
Abstract: In this work we establish that the Inozemtsev system is the SeibergWitten integrable system encoding the Coulomb branch physics of 4d \cN=2 USp(2N) gauge theory with four fundamental and (for N≥2) one antisymmetric tensor hypermultiplets. We describe the transformation from the spectral curves and canonical oneform of the Inozemtsev system in the N=1 and N=2 cases to the SeibergWitten curves and differentials explicitly, along with the explicit matching of the modulus of the elliptic curve of spectral parameters to the gauge coupling of the field theory, and of the couplings of the Inozemtsev system to the field theory mass parameters. This result is a particular instance of a more general correspondence between crystallographic elliptic CalogeroMoser systems with SeibergWitten integrable systems, which will be explored in future work.