Publications 2020

Authors: Agnese Bissi, Andrea Manenti and Alessandro Vichi

Preprint number: UUITP-46/20

We perform a numerical bootstrap study of the mixed correlator system containing the half-BPS operators of dimension two and three in N = 4 Super Yang-Mills. 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 R-symmetry 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.

Authors: Agnese Bissi, Giulia Fardelli, Alessandro Georgoudis

Preprint number: UUITP-45/20

Abstract: We computed a set of structures which appear in the four-point 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 s-cuts. We made several checks and
we conjecture that the same interpretation holds for supergravity amplitudes on AdS5×S5

Authors: Thomas Van Riet

Preprint number: UUITP-44/20

Abstract: In the context of the Weak Gravity Conjecture the notion of quasi-extremality 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 no-force 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 quasi-extremality 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 self-repulsive in a Euclidean sense.

Authors: Jan E. Gerken, Axel Kleinschmidt, Carlos R. Mafra, Oliver Schlotterer, Bram Verbeek

Preprint number: UUITP-43/20

We relate the low-energy expansions of world-sheet integrals in genus-one amplitudes of open- and closed-string states. The respective expansion coefficients are elliptic multiple zeta values in the open-string case and non-holomorphic modular forms dubbed ``modular graph forms'' for closed strings. By inspecting the differential equations and degeneration limits of suitable generating series of genus-one 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 single-valued map which generalizes the genus-zero notion of a single-valued map acting on multiple zeta values seen in tree-level relations between the open and closed string.

Authors: Magdalena Larfors, Davide Passaro, Robin Schneider

Preprint number: UUITP-42/20

Abstract: The systematic program of heterotic line bundle model building has resulted
in a wealth of standard-like 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.

Authors: Nikolay Gromov, Fedor Levkovich-Maslyuk, Paul Ryan, Dmytro Volin

Preprint number: UUITP-41/20

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 higher-rank 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 Q-functions and their dual.

Authors: Paul Ryan, Dmytro Volin

Preprint number: UUITP-40/20

Abstract: We propose a way to separate variables in a rational integrable gl(n) spin chain with an arbitrary finite-dimensional irreducible representation at each site and with generic twisted periodic boundary conditions. Firstly, we construct a basis that diagonalises a higher-rank version of the Sklyanin B-operator; 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 Gelfand-Tsetlin patterns. Then, we show that the same basis can be equivalently constructed by action of Bäcklund-transformed fused transfer matricies, whence the Bethe wave functions factorise into a product of ascending Slater determinants in Baxter Q-functions. Finally, we construct raising and lowering operators -- the conjugate momenta -- as normal-ordered Wronskian expressions in Baxter Q-operators 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.

Authors: Dmitry Chernyak, Sebastien Leurent, Dmytro Volin

Preprint number: UUITP-39/20

We consider rational integrable supersymmetric gl(m|n) 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 Q-functions 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 twist-less 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 twist-less chain where we succeed to provide explicit solutions and their systematic labelling with standard Young tableaux.

Authors: Eric D'Hoker, Oliver Schlotterer

Preprint number: UUITP-36/20

Higher genus modular graph tensors map Feynman graphs to functions on the Torelli space of genus-h 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 one-loop and tree-level modular graph tensors are proven for arbitrary genus and arbitrary tensorial rank.

Authors: Simon Ekhammar, Hongfei Shu, Dmytro Volin

Preprint number: UUITP-35/20

Abstract: 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 Q-system that comprise Q-vectors in each of the fundamental representations of the (Langlands dual of) the underlying symmetry algebra. These Q-vectors 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 finite-difference oper, explicit equivalence depends on (an arbitrary choice of) a Coxeter element. The paper considers the case of simple Lie algebras with a simply-laced 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 Q-functions and give the explicit character solution of the extended Q-system in the Dr case. We also show how to build up the extended Q-system 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 Q-functions of the extended Q-system. We conjecture that the extended Q-system 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.

Authors: Michele Del Zotto, and Kantaro Ohmori

Preprint number: UUITP-34/20

Authors: Souvik Banerjee, Ulf Danielsson, Suvendu Giri

Preprint number: UUITP-33/20

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 Randall-Sundrum model of brane-localized 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.

Authors: Michele Levi and Fei Teng

Preprint number: UUITP-32/20

Abstract: In this work we derive for the first time the complete gravitational 
quartic-in-spin effective action at the next-to-leading 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 post-Newtonian (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 four-velocity. 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 even-parity 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.

Author: Adam Bzowski

Preprint number: UUITP-30/20

We introduce a new coupling between stress tensors of the CFTs living on the two boundaries of the BTZ black hole. Similar to the TT-bar-deformation, 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.

Authors: Eric D'Hoker, Carlos R. Mafra, Boris Pioline, Oliver Schlotterer

Preprint number: UUITP-29/20

Abstract: In an earlier paper, we constructed the genus-two 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 genus-two modular graph functions, generalizing those already encountered for four external massless states. To leading and sub-leading 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 non-linear 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 genus-two modular graph functions, which we prove, ensures that up to order D^6 R^5, the five-point amplitudes require only a single new modular graph function in addition to those needed for the four-point amplitude. We check that the supergravity limit of U(1)_R-violating 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 five-point amplitude, and pave the way for understanding S-duality beyond the BPS-protected sector.

Authors: P.S. Howe and U. Lindström

Preprint number: UUITP-28/20

Abstract:

Author: Aidan Herderschee and Fei Teng

Preprint number: UUITP-27/20

Abstract: We continue the study of open associahedra associated with bi-color 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.

Authors: Michele Del Zotto, Iñaki García Etxebarria, Saghar S. Hosseini

Preprint number: UUITP - 26/20

We determine the structure of 1-form 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 Argyres-Douglas theories and many others. Despite the lack of known gauge theory descriptions for most such theories, we find that the spectrum of 1-form symmetries can be obtained via a careful analysis of the non-commutative 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′) Argyres-Douglas theories found by Cecotti-Neitzke-Vafa. In those cases where N=1 gauge theory descriptions have been proposed for theories within this class, we find agreement between the 1-form symmetries of such N=1 Lagrangian flows and those of the actual Argyres-Douglas fixed points, thus giving a consistency check for these proposals.

Authors: Luca Cassia, Rebecca Lodin and Maxim Zabzine

Preprint number: UUITP-25/20

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.

Authors: Guido Festuccia and Maxim Zabzine

Preprint number: UUITP-24/20

Abstract:
We perform a systematic study of S-duality for N=2 supersymmetric non-linear abelian theories on a curved manifold. Localization can be used to compute certain supersymmetric observables in these theories. We point out that localization and S-duality acting as a Legendre transform are not compatible. For these theories S-duality 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 non-abelian supersymmetric theory.

Authors: Joseph A. Minahan and Anton Nedelin

Preprint number: UITP-23/20

Authors: Johannes Broedel, André Kaderli, Oliver Schlotterer

Preprint number: UUITP-22/20

Abstract: Two different constructions generating the low-energy expansion of genus-one moduli-space integrals appearing in one-loop open-string amplitudes have been put forward in refs. [1,2]. We are going to show that both approaches can be traced back to an elliptic Knizhinik--Zamolodchikov--Bernard (KZB) system on the twice-punctured torus. 

We derive an explicit all-multiplicity 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.

Authors: Parijat Dey, Tobias Hansen, Mykola Shpot

Preprint number: UUITP-21/20

We show that in boundary CFTs, there exists a one-to-one correspondence between the boundary operator expansion of the two-point 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 two-point 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 4-epsilon dimensional semi-infinite space to order O(epsilon). The bulk operator product expansion of the two-point 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 large-N expansions.

Authors: Diego García Sepúlveda and Max Guillen

Preprint number: UUITP-20/20

We present a novel ten-dimensional 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 quantum-mechanical 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 super-Yang-Mills interactions. After extending the pure spinor twistor transform to include an additional supersymmetry, our results are immediately generalized to Type IIB supergravity.

Authors: Diego García Sepúlveda and Max Guillen

Preprint number: UUITP-19/20

We present a novel twistor formulation of the ten-dimensional 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 super-Pauli-Lubanski three-form naturally arises as a constraint. Quantization is studied in detail for both models and they are shown to correctly describe the D=10 super-Yang-Mills states.

Authors: Max Guillen

Preprint number: UUITP-18/20

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 non-minimal 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 non-Lorentz covariant b-ghost, ghost number zero and two vertex operators satisfying standard descent equations will be presented in full form.

Authors: Rodolfo Panerai, Antonio Pittelli, Konstantina Polydorou

Preprint number: UUITP-17/20

We find a one-dimensional protected subsector of N = 4 matter theories on a general class of three-dimensional 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 one-dimensional action with support on the fixed-point 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 three-dimensional theory to general N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

Authors: Eric D'Hoker, Carlos R. Mafra, Boris Pioline, Oliver Schlotterer

Preprint number: UUITP-16/20

Abstract: The full two-loop amplitudes for five massless states in Type II and Heterotic superstrings are constructed in terms of convergent integrals over the genus-two 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 S-duality are relegated to a first companion paper. A construction from first principles in the RNS formulation of the genus-two amplitude with five external NS states is relegated to a second companion paper.

Authors: Federica Albertini, Michele Del Zotto, Iñaki García Etxebarria, Saghar S. Hosseini

Preprint number: UUITP-15/20

Abstract: We discuss the geometric origin of discrete higher form symmetries of quantum field theories in terms of defect groups from geometric engineering in M-theory. The flux non-commutativity in M-theory 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 well-known 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 1-form center symmetry and the magnetic 4-form center symmetry in the defect group. The case of five-dimensional SCFTs from M-theory on toric singularities is discussed in detail. In that context we determine the corresponding 1-form and 2-form defect groups and we explain how to determine the corresponding mixed 't Hooft anomalies from flux non-commutativity. Several predictions for non-conventional 5d SCFTs are obtained. The matching of discrete higher-form symmetries and their anomalies provides an interesting consistency check for 5d dualities.

Authors: Markus Dierigl, Paul-Konstantin Oehlmann, Fabian Ruehle

Preprint number: UUITP-14/20

Abstract: Six-dimensional N=(1,0) superconformal field theories can be engineered geometrically via F-theory on elliptically-fibered Calabi-Yau 3-folds. 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 non-trivial, finite Mordell-Weil group, which allows us to identify the full non-Abelian 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 M-theory description, in which our configurations are interpreted as generalizations of discrete holonomy instantons.

Author: Adam Bzowski

Preprint number: UUITP-13/20

Abstract: I present a Mathematica package designed for manipulations and evaluations of triple-K integrals and conformal correlation functions in momentum space. Additionally, the program provides tools for evaluation of a large class of 2- and 3-point massless multi-loop Feynman integrals with generalized propagators. The package is accompanied by five Mathematica notebooks containing detailed calculations of numerous conformal 3-point functions in momentum space.

Authors: Alex Edison and Fei Teng

Preprint number: UUITP-12/20

Abstract: In this paper, we propose an improved method for directly calculating
double-copy-compatible tree numerators in (super-)Yang-Mills and Yang-Mills-scalar
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 one-loop 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 minimally-coupled massive particles potentially useful for future com-
putations in both classical and quantum gravity.

Authors: Alex Edison, Song He, Oliver Schlotterer, Fei Teng

Preprint number: UUITP-11/20

We present new formulas for one-loop ambitwistor-string 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 all-multiplicity expressions for tree-level two-fermion correlators in the RNS formalism that closely resemble the purely bosonic ones. After taking forward limits of tree-level correlators with an additional pair of fermions/bosons, one-loop 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 parity-odd contributions from forward limits with chiral fermions. One-loop numerators satisfying the Bern-Carrasco-Johansson (BCJ) duality for diagrams with linearized propagators can be extracted from such correlators using the well-established tree-level techniques in Yang-Mills theory coupled to biadjoint scalars. Finally, we obtain streamlined expressions for BCJ numerators up to seven points using multiparticle fields.

Authors: Guido Festuccia, Anastasios Gorantis, Antonio Pittelli, Konstantina Polydorou and Lorenzo Ruggeri

Preprint number: UUITP-10/20

We construct a large class of gauge theories with extended supersymmetry on four-dimensional 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 self-duality for two-forms 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.

Authors: Jan E. Gerken, Axel Kleinschmidt, Oliver Schlotterer

Preprint number: UUITP-09/20

We study generating series of torus integrals that contain all so-called modular graph forms relevant for massless one-loop closed-string amplitudes. By analysing the differential equation of the generating series we construct a solution for its low-energy expansion to all orders in the inverse string tension $\alpha'$. Our solution is expressed through initial data involving multiple zeta values and certain real-analytic 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 real-analytic modular forms. We study the properties of our real-analytic 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.

Authors: Ulf Lindström and Martin Rocek

Preprint number: UUITP-08/20

Abstract:

We find a geometric description of interacting beta-gamma systems as a null Kac-Moody quotient of a nonlinear sigma-model for systems with varying amounts of supersymmetry.

Authors: Nikolaos Iakovidis, Jian Qiu, Andreas Rocén, Maxim Zabzine

Preprint number: UUITP-06/20

Abstract: We study 7D maximally supersymmetric Yang-Mills theory on 3-Sasakian manifolds. For manifolds whose hyper-Kähler 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.

Author: Magdalena Larfors and Robin Schneider

Preprint number: UUITP-05/20

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 $h^{(1,1)}$.

Author: Usman Naseer

Preprint number: UUITP-04/20

In local quantum field theory on a background spacetime, the entanglement entropy of a region is divergent due to the arbitrary short-wavelength 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 one-loop Renyi partition functions by considering the theory on a simple branched cover of the configuration space of closed strings. The short-wavelength modes are cut off at the string scale and the one-loop entanglement entropy is ultraviolet-finite.  A non-canonical kinetic term in string field theory, required to produce the correct one-loop vacuum amplitude, plays a key role.

Authors: A. Bissi, G. Fardelli, A. Georgoudis

Preprint number: UUITP-03/20

We study the four point function of the superconformal primary of the stress-tensor 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.

Authors: Giuseppe Dibitetto, Nicolò Petri, Marjorie Schillo

Preprint number: UUITP-2/20

Abstract: We study non-perturbative 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 lower-dimensional de Sitter geometry within a non-compact 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.

Authors: Souvik Banerjee, Ulf Danielsson, Suvendu Giri

Preprint number: UUITP-1/20

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 brane-bending, 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.