Publications 2020

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

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 N=(1,0) superconformal field theories can be engineered geometrically via Ftheory on ellipticallyfibered CalabiYau 3folds. However, up to now this geometric framework has only been utilized to derive the flavor and gauge algebras on the tensor branch of such theories. Here, we include the presence of torsional sections that lead to a nontrivial, finite MordellWeil group, which allows us to identify the full nonAbelian group structure rather than just the algebra. The presence of torsion 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.