Publikationer 2020

The perturbative CFT optical theorem and highenergy string scattering in AdS at one loop
Authors: António Antunes, Miguel Costa, Tobias Hansen, Aaditya Salgarkar, Sourav Sarkar
Preprint number: UUITP52/20
Abstract: We derive an optical theorem for perturbative CFTs which computes the double discontinuity of conformal correlators from the single discontinuities of lower order correlators, in analogy with the optical theorem for flat space scattering amplitudes. The theorem takes a purely multiplicative form in the CFT impact parameter representation used to describe highenergy scattering in the dual AdS theory. We use this result to study fourpoint correlation functions that are dominated in the Regge limit by the exchange of the graviton Regge trajectory (Pomeron) in the dual theory. At oneloop the scattering is dominated by double Pomeron exchange and receives contributions from tidal excitations of the scattering states which are efficiently described by an AdS vertex function, in close analogy with the known Regge limit result for oneloop string scattering in flat space at finite string tension. We compare the flat space limit of the conformal correlator to the flat space results and thus derive constraints on the oneloop vertex function for type IIB strings in AdS and also on general spinning tree level type IIB amplitudes in AdS.

Spontaneous symmetry breaking in free theories with boundary potentials
Authors: Vladimír Procházka, Alexander Söderberg
Preprint number: UUITP 50/20
Abstract: Patterns of symmetry breaking induced by potentials at the boundary of free $O(N)$ models in $d=3 \epsilon$ dimensions are studied. We show that the spontaneous symmetry breaking in these theories leads to a boundary RG flow ending with $N  1$ Neumann modes in the IR. The possibility of fluctuationinduced symmetry breaking is examined and we derive a general formula for computing oneloop effective potentials at the boundary. Using the $\epsilon$expansion we test these ideas in an $O(N)\oplus O(N)$ model with boundary interactions. We determine the RG flow diagram of this theory and find that it has an IRstable critical point satisfying conformal boundary conditions. The leading correction to the effective potential is computed and we argue the existence of a phase boundary separating the region flowing to the symmetric fixed point from the region flowing to a symmetrybroken phase with a combination of Neumann and Dirchlet boundary conditions.

Conformal field theories on deformed spheres, anomalies, and supersymmetry
Joseph A. Minahan, Usman Naseer and Charles Thull
Preprint number:UUITP51/20
We study the free energy of fourdimensional CFTs on deformed spheres. For generic nonsupersymmetric CFTs only the coefficient of the logarithmic divergence in the free energy is physical, which is an extremum for the round sphere. We then specialize to $\NN=2$ SCFTs where one can preserve some supersymmetry on a compact manifold by turning on appropriate background fields. For deformations of the round sphere the $c$ anomaly receives corrections proportional to the supersymmetric completion of the (Weyl)$^2$ term, which we determine up to one constant by analyzing the scale dependence of various correlators in the stresstensor multiplet. We further show that the double derivative of the free energy with respect to the marginal couplings is proportional to the twopoint function of the bottom components of the marginal chiral multiplet placed at the two poles of the deformed sphere. We then use anomaly considerations and counterterms to parametrize the finite part of the free energy which makes manifest its dependence on the Kähler potential. We demonstrate these results for a theory with a vector multiplet and a massless adjoint hypermultiplet using results from localization. Finally, by choosing a special value of the hypermultiplet mass where the free energy is independent of the deformation, we derive an infinite number of constraints between various integrated correlators in N=4 super YangMills with any gauge group and at all values of the coupling, extending previous results.

Consistency of supersymmetric 't Hooft anomalies
Preprint number: UUITP 48/20
Authors: Adam Bzowski, Guido Festuccia, Vladimir Prochazka
Abstract: We consider recent claims that supersymmetry is anomalous in the presence
of a Rsymmetry anomaly. We revisit arguments that such an anomaly in supersymmetry
can be removed and write down an explicit counterterm that accomplishes it. Removal of
the supersymmetry anomaly results in extra terms in the Ward identities for other anomalous
symmetries. We show how WessZumino consistency conditions are modi ed when
the anomaly is removed. Finally we check that the modi ed WessZumino consistency
conditions are satis ed, and supersymmetry unbroken, in an explicit one loop computation
using PauliVillars regulators. For this purpose we comment on how to use PauliVillars
to regulate correlators of components of the supercurrent multiplet in a manifestly supersymmetric
way. 
RozanskyWitten theory, Localised then Tilted
Author: Jian Qiu
Preprint number UUITP 47/20
The paper is motivated by a very curious preprint \cite{Gukov:2020lqm}, where the equivariant index formula for the dimension of the Hilbert space of the RozanskyWitten theory is interpreted as some Verlinde formula. In this interpretation, the fixed points of target HyperK\"ahler geometry correspond to certain 'states'. In the first part of the current paper, we apply the localisation technique to the RozanskyWitten theory via first reformulating the latter as some supersymmetric sigmamodel. We obtain the exact formula for the partition function on $S^1\times\Sigma_g$ and the lens spaces. The second part extends the formalism to incorporate equivariance on the target geometry. We then apply the tilting theory to the derived category of coherent sheave on the noncompact HyperK\"ahler variety, which allows us to pick a 'basis' for the Wilson loops in the theory. We can then compute the fusion products in this basis and we show that the objects that have diagonal fusion rules are intimately related to the fixed points of the geometry. Using these objects as basis to compute the dimension of the Hilbert space leads back to the equivariant index theorem, thus answering the question that motivated the paper.

Bootstrapping mixed correlators in N=4 Super YangMills
Authors: Agnese Bissi, Andrea Manenti and Alessandro Vichi
Preprint number: UUITP46/20
We perform a numerical bootstrap study of the mixed correlator system containing the halfBPS operators of dimension two and three in N = 4 Super YangMills. This setup improves on previous works in the literature that only considered single correlators of one or the other operator. We obtain upper bounds on the leading twist in a given representation of the Rsymmetry by imposing gaps on the twist of all operators rather than the dimension of a single one. As a result we find a tension between the large N supergravity predictions and the numerical finite N results already at N~100. A few possible solutions are discussed: the extremal spectrum suggests that at large but finite N, in addition to the double trace operators, there exists a second tower of states with smaller dimension.
We also obtain new bounds on the dimension of operators which were not accessible with a single correlator setup.
Finally we consider bounds on the OPE coefficients of various operators.
The results obtained for the OPE coefficient of the lightest scalar singlet show evidences of a two dimensional conformal manifold.

All loop structures in Supergravity Amplitudes on AdS5×S5 from CFT
Authors: Agnese Bissi, Giulia Fardelli, Alessandro Georgoudis
Preprint number: UUITP45/20
Abstract: We computed a set of structures which appear in the fourpoint function of
protected operators of dimension two in N = 4 Super Yang Mills with SU (N) gauge group,
at any order in a large N expansion. They are determined only by leading order CFT data.
By focusing on a specific limit, we made connection with the dual supergravity amplitude in
flat space, where such structures correspond to iterated scuts. We made several checks and
we conjecture that the same interpretation holds for supergravity amplitudes on AdS5×S5 
A comment on noforce conditions for black holes and branes
Authors: Thomas Van Riet
Preprint number: UUITP44/20
Abstract: In the context of the Weak Gravity Conjecture the notion of quasiextremality for black holes and branes was recently defined as the property of having either vanishing horizon size or surface gravity. It was derived that such objects obey a noforce condition. In this short note I present a simplified derivation that is essentially present in the formalism of timelike reduction pioneered by Breitenlohner, Gibbons and Maison. This formalism also provides the natural definition of quasiextremality for gravitational instantons (and wormholes) sourced by axion fluxes and strengthens the argument that macroscopic axion wormholes do not contribute in the path integral since they are selfrepulsive in a Euclidean sense.

Towards closed strings as singlevalued open strings at genus one
Authors: Jan E. Gerken, Axel Kleinschmidt, Carlos R. Mafra, Oliver Schlotterer, Bram Verbeek
Preprint number: UUITP43/20
We relate the lowenergy expansions of worldsheet integrals in genusone amplitudes of open and closedstring states. The respective expansion coefficients are elliptic multiple zeta values in the openstring case and nonholomorphic modular forms dubbed ``modular graph forms'' for closed strings. By inspecting the differential equations and degeneration limits of suitable generating series of genusone integrals, we identify formal substitution rules mapping the elliptic multiple zeta values of open strings to the modular graph forms of closed strings. Based on the properties of these rules, we refer to them as an elliptic singlevalued map which generalizes the genuszero notion of a singlevalued map acting on multiple zeta values seen in treelevel relations between the open and closed string.

Heterotic Line Bundle Models on Generalized Complete Intersection Calabi Yau Manifolds
Authors: Magdalena Larfors, Davide Passaro, Robin Schneider
Preprint number: UUITP42/20
Abstract: The systematic program of heterotic line bundle model building has resulted
in a wealth of standardlike models (SLM) for particle physics. In this paper,
we continue this work in the setting of generalised Complete Intersection
Calabi Yau (gCICY) manifolds. Using the gCICYs constructed in Ref. [1], we
identify two geometries that, when combined with line bundle sums, are directly
suitable for heterotic GUT models. We then show that these gCICYs admit freely
acting $\mathbb{Z}_2$ symmetry groups, and are thus amenable to Wilson line
breaking of the GUT gauge group to that of the standard model. We proceed to a
systematic scan over line bundle sums over these geometries, that result in 99
and 33 SLMs, respectively. For the first class of models, our results may be
compared to line bundle models on homotopically equivalent Complete
Intersection Calabi Yau manifolds. This shows that the number of realistic
configurations is of the same order of magnitude. 
Dual Separated Variables and Scalar Products
Authors: Nikolay Gromov, Fedor LevkovichMaslyuk, Paul Ryan, Dmytro Volin
Preprint number: UUITP41/20
Abstract: Separation of variables (SoV) is an extremely efficient and elegant technique for analysing physical systems but its application to integrable spin chains was limited until recently to the simplest su(2) cases. In this paper we continue developing the SoV program for higherrank spin chains and demonstrate how to derive the measure for the su(3) case. Our results are a natural consequence of factorisability of the wave function and functional orthogonality relations following from the interplay between Baxter equations for Qfunctions and their dual.

Separation of variables for rational gl(n) spin chains in any compact representation, via fusion, embedding morphism and Backlund flow
Authors: Paul Ryan, Dmytro Volin
Preprint number: UUITP40/20
Abstract: We propose a way to separate variables in a rational integrable gl(n) spin chain with an arbitrary finitedimensional irreducible representation at each site and with generic twisted periodic boundary conditions. Firstly, we construct a basis that diagonalises a higherrank version of the Sklyanin Boperator; the construction is based on recursive usage of an embedding of a gl(k) spin chain into a gl(k+1) spin chain which is induced from a Yangian homomorphism and controlled by dual diagonals of GelfandTsetlin patterns. Then, we show that the same basis can be equivalently constructed by action of Bäcklundtransformed fused transfer matricies, whence the Bethe wave functions factorise into a product of ascending Slater determinants in Baxter Qfunctions. Finally, we construct raising and lowering operators  the conjugate momenta  as normalordered Wronskian expressions in Baxter Qoperators evaluated at zeros of B  the separated variables. It is an immediate consequence of the proposed construction that the Bethe algebra comprises the maximal possible number of mutually commuting charges  a necessary property for Bethe equations to be complete.

Completeness of Wronskian Bethe equations for rational gl(mn) spin chains
Authors: Dmitry Chernyak, Sebastien Leurent, Dmytro Volin
Preprint number: UUITP39/20
We consider rational integrable supersymmetric gl(mn) spin chains in the defining representation and prove the isomorphism between a commutative algebra of conserved charges (the Bethe algebra) and a polynomial ring (the Wronskian algebra) defined by functional relations between Baxter Qfunctions that we call Wronskian Bethe equations. These equations, in contrast to standard nested Bethe equations, admit only physical solutions for any value of inhomogeneities and furthermore we prove that the algebraic number of solutions to these equations is equal to the dimension of the spin chain Hilbert space (modulo relevant symmetries). Both twisted and twistless periodic boundary conditions are considered, the isomorphism statement uses, as a sufficient condition, that the spin chain inhomogeneities \theta_\ell satisfy \theta_\ell+\hbar\neq\theta_{\ell'} for \ell<\ell'. Counting of solutions is done in two independent ways: by computing a character of the Wronskian algebra and by explicitly solving the Bethe equations in certain scaling regimes supplemented with a proof that the algebraic number of solutions is the same for any value of \theta_\ell. In particular, we consider the regime \theta_{\ell+1}/\theta_{\ell}\gg ≫1 for the twistless chain where we succeed to provide explicit solutions and their systematic labelling with standard Young tableaux.

Identities among higher genus modular graph tensors
Authors: Eric D'Hoker, Oliver Schlotterer
Preprint number: UUITP36/20
Higher genus modular graph tensors map Feynman graphs to functions on the Torelli space of genush compact Riemann surfaces which transform as tensors under the modular group Sp(2h,Z), thereby generalizing a construction of Kawazumi. An infinite family of algebraic identities between oneloop and treelevel modular graph tensors are proven for arbitrary genus and arbitrary tensorial rank.

Extended systems of Baxter Qfunctions and fused flags I: simplylaced case
Authors: Simon Ekhammar, Hongfei Shu, Dmytro Volin
Preprint number: UUITP35/20Abstract: The spectrum of integrable models is often encoded in terms of commuting functions of a spectral parameter that satisfy functional relations. We propose to describe this commutative algebra in a covariant way by means of the extended Qsystem that comprise Qvectors in each of the fundamental representations of the (Langlands dual of) the underlying symmetry algebra. These Qvectors turn out to parameterise a collection of complete flags which are fused with one another in a particular way. We show that the fused flag is gauge equivalent to a finitedifference oper, explicit equivalence depends on (an arbitrary choice of) a Coxeter element. The paper considers the case of simple Lie algebras with a simplylaced Dynkin diagram. For the Ar series, the construction coincides with already known results in the literature. We apply the proposed formalism to the case of the Dr series and the exceptional algebras E_r, r=6,7,8. In particular, we solve Hirota bilinear equations in terms of Qfunctions and give the explicit character solution of the extended Qsystem in the Dr case. We also show how to build up the extended Qsystem of Dr type starting either from vectors, by a procedure similar to the A_r scenario which however constructs a fused flag of isotropic spaces, or from pure spinors, via fused Fierz relations. Finally, for the case of rational, trigonometric, and elliptic spin chains, we propose an explicit ansatz for the analytic structure of Qfunctions of the extended Qsystem. We conjecture that the extended Qsystem constrained in such a way is always in bijection with actual Bethe algebra of commuting transfer matrices of these models and moreover can be used to show that the Bethe algebra has a simple joint spectrum.

2group symmetries of 6d little string theories and Tduality
Authors: Michele Del Zotto, and Kantaro Ohmori
Preprint number: UUITP34/20
We determine the 2group structure constants for all the sixdimensional little string theories (LSTs) geometrically engineered in Ftheory without frozen singularities. We use this result as a consistency check for Tduality: the 2groups of a pair of Tdual LSTs have to match. When the Tduality involves a discrete symmetry twist the 2group used in the matching is modified. We demonstrate the matching of the 2groups in several examples.

Bubble needs strings
Authors: Souvik Banerjee, Ulf Danielsson, Suvendu Giri
Preprint number: UUITP33/20
Abstract: In this paper, we want to emphasize the pivotal role played by strings in the model realizing de Sitter using an expanding bubble, proposed and subsequently developed in arXiv:1807.01570, arXiv:1907.04268, and arXiv:2001.07433. Contrary to the RandallSundrum model of branelocalized gravity, we use the end points of radially stretched strings to obtain matter sourcing gravity induced on the bubble wall. This allows us to reinterpret the possible volume divergence coming from naive dimensional reduction as mass renormalization in four dimensional particle physics. Furthermore, we argue that the residual time dependence in the bulk, pointed out by some recent work as a possible shortcoming of such models, is automatically cured in presence of these stringy sources.

NLO gravitational quarticinspin interaction
Authors: Michele Levi and Fei Teng
Preprint number: UUITP32/20
Abstract: In this work we derive for the first time the complete gravitational
quarticinspin effective action at the nexttoleading order for the
interaction of generic compact binaries via the effective field theory
for gravitating spinning objects and its extension to this sector. This
sector, which enters at the fifth postNewtonian (5PN) order
for rapidly rotating compact objects, completes finite size effects up to
this order, beyond the current state of the art for generic compact binary dynamics
at the 4PN order.
At this order in spins with gravitational nonlinearities we have to take into
account additional terms, which arise from a new type of worldline
couplings, due to the fact that at this order the Tulczyjew gauge for the
rotational degrees of freedom, which involves the linear momentum, can no
longer be approximated only in terms of the fourvelocity. One of the main
motivations for us to tackle this sector is also to see what happens when
we go to a sector, which corresponds to the gravitational Compton
scattering with quantum spins of two, and possibly also get
an insight on the inability to uniquely fix its amplitude when spins
of five halves and higher are involved. A general
observation that we can clearly make already is that evenparity sectors
in the order of the spin are easier to handle than odd ones. In the
quantum context this corresponds to the greater ease of dealing with
bosons compared to fermions. 
Conformal correlators as simplex integrals in momentum space
Authors: Adam Bzowski, Paul McFadden, Kostas Skenderis
Preprint number: UUITP31/20
We find the general solution of the conformal Ward identities for scalar npoint functions in momentum space and in general dimension. The solution is given in terms of integrals over (n−1)simplices in momentum space. The n operators are inserted at the n vertices of the simplex, and the momenta running between any two vertices of the simplex are the integration variables. The integrand involves an arbitrary function of momentumspace cross ratios constructed from the integration variables, while the external momenta enter only via momentum conservation at each vertex. Correlators where the function of cross ratios is a monomial exhibit a remarkable recursive structure where npoint functions are built in terms of (n−1)point functions. To illustrate our discussion, we derive the simplex representation of npoint contact Witten diagrams in a holographic conformal field theory. This can be achieved through both a recursive method, as well as an approach based on the starmesh transformation of electrical circuit theory. The resulting expression for the function of cross ratios involves (n−2) integrations, which is an improvement (when n>4) relative to the Mellin representation that involves n(n−3)/2 integrations.

Wormholes from twosided TTbardeformation
Author: Adam Bzowski
Preprint number: UUITP30/20
We introduce a new coupling between stress tensors of the CFTs living on the two boundaries of the BTZ black hole. Similar to the TTbardeformation, the system exhibits universal properties and is solvable. The resulting geometry is an extreme case of a wormhole with the right and left BTZ wedges glued together along the horizons. We show that the geometry is realized by uniform shock waves emanating from both asymptotic boundaries. The construction has profound implications for the structure of the Hilbert space of states of the dual QFT.

Twoloop superstring fivepoint amplitudes II: Low energy expansion and Sduality
Authors: Eric D'Hoker, Carlos R. Mafra, Boris Pioline, Oliver Schlotterer
Preprint number: UUITP29/20
Abstract: In an earlier paper, we constructed the genustwo amplitudes for five external massless states in Type II and Heterotic string theory, and showed that the $\alpha'$ expansion of the Type II amplitude reproduces the corresponding supergravity amplitude to leading order. In this paper, we analyze the effective interactions induced by Type II superstrings beyond supergravity, both for U(1)_R preserving amplitudes such as for five gravitons, and for U(1)_R violating amplitudes such as for one dilaton and four gravitons. At each order in alpha', the coefficients of the effective interactions are given by integrals over moduli space of genustwo modular graph functions, generalizing those already encountered for four external massless states. To leading and subleading orders, the coefficients of the effective interactions D^2 R^5 and D^4 R^5 are found to match those of D^4 R^4 and D^6 R^4, respectively, as required by nonlinear supersymmetry. To the next order, a D^6 R^5 effective interaction arises, which is independent of the supersymmetric completion of D^8 R^4, and already arose at genus one. A novel identity on genustwo modular graph functions, which we prove, ensures that up to order D^6 R^5, the fivepoint amplitudes require only a single new modular graph function in addition to those needed for the fourpoint amplitude. We check that the supergravity limit of U(1)_Rviolating amplitudes is free of UV divergences to this order, consistently with the known structure of divergences in Type IIB supergravity. Our results give strong consistency tests on the full fivepoint amplitude, and pave the way for understanding Sduality beyond the BPSprotected sector.

Local supertwistors and conformal supergravity in six dimensions
Författare: P.S. Howe and U. Lindström
Preprintnummer :UUITP28/20
Abstract:
The local supertwistor formalism, which involves a superconformal connection act ing on the bundle of such objects over superspace, is used to investigate superconformal geometry in six dimensions. The geometry corresponding to (1, 0) and (2, 0) offshell conformal supergravity multiplets, as well the associated finite superWeyl transformations, are derived.

Open associahedra and scattering forms
Author: Aidan Herderschee and Fei Teng
Preprint number: UUITP27/20
Abstract: We continue the study of open associahedra associated with bicolor scatteringamplitudes initiated in arXiv:1912.08307. We focus on the facet geometries of the open associahedra,uncovering many new phenomena such fiber geometries. We then provide novel recursionprocedures for calculating the canonical form of open associahedra, generalizing recursionrelations for bounded polytopes to unbounded polytopes.

Higher Form Symmetries of ArgyresDouglas Theories
Authors: Michele Del Zotto, Iñaki García Etxebarria, Saghar S. Hosseini
Preprint number: UUITP  26/20
We determine the structure of 1form symmetries for all 4d N=2 theories that have a geometric engineering in terms of type IIB string theory on isolated hypersurface singularities. This is a large class of models, that includes ArgyresDouglas theories and many others. Despite the lack of known gauge theory descriptions for most such theories, we find that the spectrum of 1form symmetries can be obtained via a careful analysis of the noncommutative behaviour of RR fluxes at infinity in the IIB setup. The final result admits a very compact field theoretical reformulation in terms of the BPS quiver. We illustrate our methods in detail in the case of the (g,g′) ArgyresDouglas theories found by CecottiNeitzkeVafa. In those cases where N=1 gauge theory descriptions have been proposed for theories within this class, we find agreement between the 1form symmetries of such N=1 Lagrangian flows and those of the actual ArgyresDouglas fixed points, thus giving a consistency check for these proposals.

On matrix models and their $q$deformations
Authors: Luca Cassia, Rebecca Lodin and Maxim Zabzine
Preprint number: UUITP25/20
Motivated by the BPS/CFT correspondence, we explore the similarities between the classical $\beta$deformed Hermitean matrix model and the $q$deformed matrix models associated to 3d $\mathcal{N}=2$ supersymmetric gauge theories on $\halfindex$ and $S_b^3$ by matching parameters of the theories. The novel results that we obtain are the correlators for the models, together with an additional result in the classical case consisting of the $W$algebra representation of the generating function. Furthermore, we also obtain surprisingly simple expressions for the expectation values of characters which generalize previously known results.

Sduality and supersymmetry on curved manifolds
Authors: Guido Festuccia and Maxim Zabzine
Preprint number: UUITP24/20
Abstract:
We perform a systematic study of Sduality for N=2 supersymmetric nonlinear abelian theories on a curved manifold. Localization can be used to compute certain supersymmetric observables in these theories. We point out that localization and Sduality acting as a Legendre transform are not compatible. For these theories Sduality should be interpreted as Fourier transform and we provide some evidence for this. We also suggest the notion of a coholomological prepotential for an abelian theory that gives the same partition function as a given nonabelian supersymmetric theory. 
Fivedimensional gauge theories on spheres with negative couplings
Authors: Joseph A. Minahan and Anton Nedelin
Preprint number: UITP23/20
We consider supersymmetric gauge theories on S^5 with a negative YangMills coupling in their large N limits. Using localization we compute the partition functions and show that the pure SU(N) gauge theory descends to an SU(N/2)_{N/2}×SU(N/2)_{−N/2}× SU(2) ChernSimons gauge theory as the inverse ’t Hooft coupling is taken to negative infinity for N even. The YangMills coupling on the SU(N/2)_{±N/2} is infinite, while that on the SU(2) goes to zero. We also show that the odd N case has somewhat different behavior. We then study the SU(N/2)_{N/2} pure ChernSimons theory. While the eigenvalue density is only found numerically, we show that its width equals 1 in units of the inverse sphere radius, which allows us to find the leading correction to the free energy when turning on the YangMills term. We then consider USp(2N) theories with an antisymmetric hypermultiplet and N_f < 8 fundamental hypermultiplets and carry out a similar analysis. We present evidence that the USp(2N) theories have a fifth order phase transition in the inverse coupling at their superconformal fixed point. Along the way we show that the oneinstanton contribution to the partition function remains exponentially suppressed at negative coupling for the SU(N) theories in the large N limit.

Two dialects for KZB equations: generating oneloop openstring integrals
Authors: Johannes Broedel, André Kaderli, Oliver Schlotterer
Preprint number: UUITP22/20
Abstract: Two different constructions generating the lowenergy expansion of genusone modulispace integrals appearing in oneloop openstring amplitudes have been put forward in refs. [1,2]. We are going to show that both approaches can be traced back to an elliptic KnizhinikZamolodchikovBernard (KZB) system on the twicepunctured torus.
We derive an explicit allmultiplicity representation of the elliptic KZB system for a vector of iterated integrals with an extra marked point and explore compatibility conditions for the two sets of algebra generators appearing in the two differential equations.

Operator expansions, layer susceptibility and twopoint functions in BCFT
Authors: Parijat Dey, Tobias Hansen, Mykola Shpot
Preprint number: UUITP21/20
We show that in boundary CFTs, there exists a onetoone correspondence between the boundary operator expansion of the twopoint correlation function and a power series expansion of the layer susceptibility. This general property allows the direct identification of the boundary spectrum and expansion coefficients from the layer susceptibility and opens a new way for efficient calculations of twopoint correlators in BCFTs. To show how it works we derive an explicit expression for the correlation function <\phi_i \phi^i> of the O(N) model at the extraordinary transition in 4epsilon dimensional semiinfinite space to order O(epsilon). The bulk operator product expansion of the twopoint function gives access to the spectrum of the bulk CFT. In our example, we obtain the averaged anomalous dimensions of scalar composite operators of the O(N) model to order O(epsilon^2). These agree with the known results both in epsilon and largeN expansions.

A Pure Spinor Twistor Description of Ambitwistor Strings
Authors: Diego García Sepúlveda and Max Guillen
Preprint number: UUITP20/20
We present a novel tendimensional description of ambitwistor strings. This formulation is based on a set of supertwistor variables involving pure spinors and a set of constraints previously introduced in the context of the D=10 superparticle. We perform a detailed quantummechanical analysis of the constraint algebra and using standard techniques we construct a BRST operator. Physical vertex operators are explicitly constructed and scattering amplitudes are shown to correctly describe D=10 superYangMills interactions. After extending the pure spinor twistor transform to include an additional supersymmetry, our results are immediately generalized to Type IIB supergravity.

A Pure Spinor Twistor Description of the D=10 Superparticle
Authors: Diego García Sepúlveda and Max Guillen
Preprint number: UUITP19/20
We present a novel twistor formulation of the tendimensional massless superparticle. This formulation is based on the introduction of pure spinor variables through a field redefinition of another model for the superparticle, and in the new description we find that the superPauliLubanski threeform naturally arises as a constraint. Quantization is studied in detail for both models and they are shown to correctly describe the D=10 superYangMills states.

Notes on the 11D pure spinor wordline vertex operators
Authors: Max Guillen
Preprint number: UUITP18/20
The construction of the ghost number zero and one vertex operators for the 11D pure spinor superparticle will be revisited. In this sense, an alternative way of defining the ghost number one vertex operator will be given after introducing a ghost number 2 operator made out of physical operators defined on the 11D nonminimal pure spinor superspace. This procedure will make explicit and transparent the relation between the ghost number three and one vertex operators. In addition, using a nonLorentz covariant bghost, ghost number zero and two vertex operators satisfying standard descent equations will be presented in full form.

Topological Rings and Surface Defects from Equivariant Cohomology
Authors: Rodolfo Panerai, Antonio Pittelli, Konstantina Polydorou
Preprint number: UUITP17/20
We find a onedimensional protected subsector of N = 4 matter theories on a general class of threedimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah–Bott–Berline–Vergne formula to the original action demonstrates that this localizes on a onedimensional action with support on the fixedpoint submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S^3. Then we apply it to the novel case of S^2 × S^1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models form a topological ring and that their correlation functions are naturally associated with a noncommutative star product. Finally, we couple the threedimensional theory to general N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixeddimensional system.

Twoloop superstring fivepoint amplitudes I: Construction via chiral splitting and pure spinors
Authors: Eric D'Hoker, Carlos R. Mafra, Boris Pioline, Oliver Schlotterer
Preprint number: UUITP16/20
Abstract: The full twoloop amplitudes for five massless states in Type II and Heterotic superstrings are constructed in terms of convergent integrals over the genustwo moduli space of compact Riemann surfaces and integrals of Green functions and Abelian differentials on the surface. The construction combines elements from the BRST cohomology of the pure spinor formulation and from chiral splitting with the help of loop momenta and homology invariance. The alpha' > 0 limit of the resulting superstring amplitude is shown to be in perfect agreement with the previously known amplitude computed in Type II supergravity. Investigations of the alpha' expansion of the Type II amplitude and comparisons with predictions from Sduality are relegated to a first companion paper. A construction from first principles in the RNS formulation of the genustwo amplitude with five external NS states is relegated to a second companion paper.

Higher Form Symmetries and Mtheory
Authors: Federica Albertini, Michele Del Zotto, Iñaki García Etxebarria, Saghar S. Hosseini
Preprint number: UUITP15/20
Abstract: We discuss the geometric origin of discrete higher form symmetries of quantum field theories in terms of defect groups from geometric engineering in Mtheory. The flux noncommutativity in Mtheory gives rise to (mixed) 't Hooft anomalies for the defect group which constrains the corresponding global structures of the associated quantum fields. We analyze the example of 4d N=1 SYM gauge theory in four dimensions, and we reproduce the wellknown classification of global structures from reading between its lines. We extend this analysis to the case of 7d N=1 SYM theory, where we recover it from a mixed 't Hooft anomaly among the electric 1form center symmetry and the magnetic 4form center symmetry in the defect group. The case of fivedimensional SCFTs from Mtheory on toric singularities is discussed in detail. In that context we determine the corresponding 1form and 2form defect groups and we explain how to determine the corresponding mixed 't Hooft anomalies from flux noncommutativity. Several predictions for nonconventional 5d SCFTs are obtained. The matching of discrete higherform symmetries and their anomalies provides an interesting consistency check for 5d dualities.

NonSimplyConnected Symmetries in 6D SCFTs
Authors: Markus Dierigl, PaulKonstantin Oehlmann, Fabian Ruehle
Preprint number: UUITP14/20
Abstract: Sixdimensional $\mathcal{N}=(1,0)$ superconformal field theories can be engineered geometrically via Ftheory on ellipticallyfibered CalabiYau 3folds. We include torsional sections in the geometry, which lead to a finite MordellWeil group. This allows us to identify the full nonAbelian group structure rather than just the algebra. The presence of torsion also modifies the center of the symmetry groups and the matter representations that can appear. This in turn affects the tensor branch of these theories. We analyze this change for a large class of superconformal theories with torsion and explicitly construct their tensor branches. Finally, we elaborate on the connection to the dual heterotic and Mtheory description, in which our configurations are interpreted as generalizations of discrete holonomy instantons.

TripleK: A Mathematica package for evaluating tripleK integrals and conformal correlation functions
Author: Adam Bzowski
Preprint number: UUITP13/20
Abstract: I present a Mathematica package designed for manipulations and evaluations of tripleK integrals and conformal correlation functions in momentum space. Additionally, the program provides tools for evaluation of a large class of 2 and 3point massless multiloop Feynman integrals with generalized propagators. The package is accompanied by five Mathematica notebooks containing detailed calculations of numerous conformal 3point functions in momentum space.

Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
Authors: Alex Edison and Fei Teng
Preprint number: UUITP12/20
Abstract: In this paper, we propose an improved method for directly calculating
doublecopycompatible tree numerators in (super)YangMills and YangMillsscalar
theories. Our new scheme gets rid of any explicit dependence on reference orderings,
restoring a form of crossing symmetry to the numerators. This in turn improves the
computational efficiency of the algorithm, allowing us to go well beyond the number
of external particles accessible with the reference order based methods. Motivated
by an upcoming study of oneloop BCJ numerators from forward limits, we explore
the generalization to include a pair of fermions. To improve the accessiblity of the
new algorithm, we provide a Mathematica package that implements the numerator
construction. The structure of the computation also provides for a straightforward
introduction of minimallycoupled massive particles potentially useful for future com
putations in both classical and quantum gravity. 
Oneloop Correlators and BCJ Numerators from Forward Limits
Authors: Alex Edison, Song He, Oliver Schlotterer, Fei Teng
Preprint number: UUITP11/20
We present new formulas for oneloop ambitwistorstring correlators for gauge theories in any even dimension with arbitrary combinations of gauge bosons, fermions and scalars running in the loop. Our results are driven by new allmultiplicity expressions for treelevel twofermion correlators in the RNS formalism that closely resemble the purely bosonic ones. After taking forward limits of treelevel correlators with an additional pair of fermions/bosons, oneloop correlators become combinations of Lorentz traces in vector and spinor representations. Identities between these two types of traces manifest all supersymmetry cancellations and the power counting of loop momentum. We also obtain parityodd contributions from forward limits with chiral fermions. Oneloop numerators satisfying the BernCarrascoJohansson (BCJ) duality for diagrams with linearized propagators can be extracted from such correlators using the wellestablished treelevel techniques in YangMills theory coupled to biadjoint scalars. Finally, we obtain streamlined expressions for BCJ numerators up to seven points using multiparticle fields.

Cohomological Localization of N = 2 Gauge Theories with Matter
Authors: Guido Festuccia, Anastasios Gorantis, Antonio Pittelli, Konstantina Polydorou and Lorenzo Ruggeri
Preprint number: UUITP10/20
We construct a large class of gauge theories with extended supersymmetry on fourdimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang–Mills theory to general N = 2 gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson–Witten theory and Pestun’s theory on S4 as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of selfduality for twoforms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.

Generating series of all modular graph forms from iterated Eisenstein integrals
Authors: Jan E. Gerken, Axel Kleinschmidt, Oliver Schlotterer
Preprint number: UUITP09/20
We study generating series of torus integrals that contain all socalled modular graph forms relevant for massless oneloop closedstring amplitudes. By analysing the differential equation of the generating series we construct a solution for its lowenergy expansion to all orders in the inverse string tension $\alpha'$. Our solution is expressed through initial data involving multiple zeta values and certain realanalytic functions of the modular parameter of the torus. These functions are built from real and imaginary parts of holomorphic iterated Eisenstein integrals and should be closely related to Brown's recent construction of realanalytic modular forms. We study the properties of our realanalytic objects in detail and give explicit examples to a fixed order in the $\ap$expansion. In particular, our solution allows for a counting of linearly independent modular graph forms at a given weight, confirming previous partial results and giving predictions for higher, hitherto unexplored weights. It also sheds new light on the topic of uniform transcendentality of the $\alpha'$expansion.

Betagamma systems interacting with sigmamodels
Authors: Ulf Lindström and Martin Rocek
Preprint number: UUITP08/20
Abstract:
We find a geometric description of interacting betagamma systems as a null KacMoody quotient of a nonlinear sigmamodel for systems with varying amounts of supersymmetry.

Covariant Hamiltonians, sigma models and supersymmetry
Author: Ulf Lindström
Preprint number: UUITP07/20
Abstract: We introduce a phase space with spinorial momenta, corresponding to fermionic derivatives, for a 2d supersymmetric (1, 1) sigma model. We show that there is a generalisation of the covariant De DonderWeyl Hamiltonian formulation on this phase space with canonical equations equivalent to the Lagrangian formulation, find the corresponding multisymplectic form and Hamiltonian multivectors. The covariance of the formulation makes it possible to see how additional non manifest supersymmetries arise in analogy to those of the Lagrangian formulation.
We then observe that an intermediate phase space Lagrangian defined on the sum of the tangent and cotanget spaces is a first order Lagrangian for the sigma model and derive additional super symmetries for this. 
7D supersymmetric YangMills on hypertoric 3Sasakian manifolds
Authors: Nikolaos Iakovidis, Jian Qiu, Andreas Rocén, Maxim Zabzine
Preprint number: UUITP06/20
Abstract: We study 7D maximally supersymmetric YangMills theory on 3Sasakian manifolds. For manifolds whose hyperKähler cones are hypertoric we derive the perturbative part of the partition function. The answer involves a special function that counts integer lattice points in a rational convex polyhedral cone determined by hypertoric data. This also gives a more geometric structure to previous enumeration results of holomorphic functions in the literature. Based on physics intuition, we provide a factorisation result for such functions. The full proof of this factorisation using index calculations will be detailed in a forthcoming paper.

Explore and Exploit with Heterotic Line Bundle Models
Author: Magdalena Larfors and Robin Schneider
Preprint number: UUITP05/20
Abstract: We use deep reinforcement learning to explore a class of heterotic $SU(5)$ GUT models constructed from line bundle sums over Complete Intersection Calabi Yau (CICY) manifolds. We perform several experiments where A3C agents are trained to search for such models. These agents significantly outperform random exploration, in the most favourable settings by a factor of 1700 when it comes to finding unique models. Furthermore, we find evidence that the trained agents also outperform random walkers on new manifolds. We conclude that the agents detect hidden structures in the compactification data, which is partly of general nature. The experiments scale well with $h^{(1,1)}$, and may thus provide the key to model building on CICYs with large $h^{(1,1)}$.

Entanglement entropy in closed string theory
Author: Usman Naseer
Preprint number: UUITP04/20
In local quantum field theory on a background spacetime, the entanglement entropy of a region is divergent due to the arbitrary shortwavelength correlations near the boundary of the region. Quantum gravitational fluctuations are expected to cut off the entropy of the ultraviolet modes. We study the entanglement entropy in closed string theory using the framework of string field theory. In particular, we compute the oneloop Renyi partition functions by considering the theory on a simple branched cover of the configuration space of closed strings. The shortwavelength modes are cut off at the string scale and the oneloop entanglement entropy is ultravioletfinite. A noncanonical kinetic term in string field theory, required to produce the correct oneloop vacuum amplitude, plays a key role.

Towards All Loop Supergravity Amplitudes on AdS_5 x S^5
Authors: A. Bissi, G. Fardelli, A. Georgoudis
Preprint number: UUITP03/20
We study the four point function of the superconformal primary of the stresstensor multiplet in four dimensional N=4 Super Yang Mills, at large 't Hooft coupling and in a large N expansion. This observable is holographically dual to four graviton amplitudes in type IIB supergravity on AdS_5 x S^5. We construct the most trascendental piece of the correlator at order N^6 and compare it with the flat space limit of the corresponding two loops amplitude. This comparison allows us to conjecture structures of the correlator/amplitude which should be present at any loop order.

Nothing really matters
Authors: Giuseppe Dibitetto, Nicolò Petri, Marjorie Schillo
Preprint number: UUITP2/20
Abstract: We study nonperturbative instabilities of AdS spacetime in General Relativity with a cosmological constant in arbitrary dimensions. In this simple setup we explicitly construct a class of gravitational instantons generalizing Witten's bubble of nothing. We calculate the corresponding Euclidean action and show that its change is finite. The expansion of these bubbles is described by a lowerdimensional de Sitter geometry within a noncompact foliation of the background spacetime. Moreover we discuss the existence of covariantly constant spinors as a possible topological obstruction for such decays to occur. This mechanism is further connected to the stability of supersymmetric vacua in string theory.

Dark bubbles: decorating the wall
Authors: Souvik Banerjee, Ulf Danielsson, Suvendu Giri
Preprint number: UUITP1/20
Abstract: Motivated by the difficulty of constructing de Sitter vacua in string theory, a new approach was proposed in arXiv:1807.01570 and arXiv:1907.04268, where four dimensional de Sitter space was realized as the effective cosmology, with matter and radiation, on an expanding spherical bubble that mediates the decay of non supersymmetric AdS5 to a more stable AdS5 in string theory. In this third installment, we further expand on this scenario by considering the backreaction of matter in the bulk and on the brane in terms of how the brane bends. We compute the back reacted metric on the bent brane as well as in the five dimensional bulk. To further illuminate the effect of branebending, we compare our results with an explicit computation of the five dimensional graviton propagator using a holographic prescription. Finally, we interpret our model using two colliding branes that allow for a full four dimensional localization of gravity.