Publications 2020

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

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.