# Joburg Workshop on Aspects of Holography

### Talks

### Abstracts

#### Alberto Cazzaniga

**Title:** Higher rank refined Donaldson-Thomas invariants and geometric engineering

**Abstract:** Geometric engineering predicts relations between invariants counting instantons on some surfaces, and Donaldson-Thomas invariants counting sheaves on Calabi-Yau threefolds. We will present some results on the threefold side concerning the generating series higher rank sheaves and discuss how they relate to some version of the Nekrasov partition function.

#### Diego Correa

**Title:** Wilson loops, ladders, and exact results [video]

**Abstract:** Wilson loops are non-local observables of crucial importance in any gauge theory, due to the physical information that can be extracted from their expectation values and correlators. In N=4 super Yang-Mills they can be studied by different theoretical tools, which in some cases allow the obtention of results that are exact in the coupling constant dependence. In this talk I am going to consider the resummation of ladder diagrams, which can be used to reveal qualitative and quantitative aspects of the Wilson loop physics in the strong coupling limit.

#### Sumit Das

**Title:** Remarks on SYK holography [video]

**Abstract:** We will discuss a proposal for building a bulk dual of the SYK model using large N collective fields.

#### Robert de Mello Koch

**Title:** Primary fields in free CFT4 [video]

**Abstract:** Counting formulae for general primary fields in free four dimensional conformal field theories of scalars and fermions are derived. These are used to count primaries which obey extremality conditions defined in terms of the dimensions and left or right spins (i.e. in terms of relations between the charges under the Cartan subgroup of SO(4,2)). The construction of primary fields for scalar field theory is mapped to a problem of determining multi-variable polynomials subject to a system of symmetry and differential constraints. For the extremal primaries, we give a construction in terms of holomorphic polynomial functions on permutation orbifolds.

#### Shinji Hirano

**Title:** Airy function and 4d quantum gravity [video]

**Abstract:** We study 4d quantum gravity with negative cosmological constant in the minisuperspace approximation and compute the partition function for the S^3 boundary geometry. In this approximation scheme the path integrals become dominated by a class of asymptotically AdS “microstate geometries.’’ Despite the fact that the theory is pure Einstein gravity without supersymmetry, the result precisely reproduces, up to higher curvature corrections, the Airy function in the S^3 partition function of the maximally supersymmetric Chern-Simons-matter (CSM) theory which sums up all perturbative 1/N corrections. We also show that this can be interpreted as a concrete realization of the idea that the CFT partition function is a solution to the Wheeler-DeWitt equation as advocated in the holographic renormalization group. Furthermore, the agreement persists upon the inclusion of a string probe and it reproduces the Airy function in the vev of half-BPS Wilson loops in the CSM theory.

#### Diego Hofman

**Title:** Generalized global symmetries: formal aspects, holography, and hydrodynamics [video]

**Abstract:** In this talk I will give an introduction to various aspects of generalized global symmetries. These are conserved p-form objects that generalize global currents given by 1-forms. I will present examples where these symmetries play an important role both in QFT and holographic setups. I will discuss their importance in gauge invariant descriptions of gauge theories, their role in classifying phases of QFTs and if there is time their hydrodynamics properties.

#### Antal Jevicki

**Title:** Maps and diagrams in bi-local holography [video]

**Abstract:** We discuss AdS Feynman/Witten Diagrams in Bi-local reconstruction of Higher Spin Theory. The question of (Non)locality will be addressed.

#### Minkyoo Kim

**Title:** Structure constants in ladder limit [video]

**Abstract:** I will talk about my recent work on structure constants of local operators inserted to 1/2-BPS Wilson line in N=4 SYM. In particular, I would like to concentrate on results in so called ladder limit which is a double scailing limit. As in this limit computing structure constants is reduced to solving a Schroedinger equation, one can obtain answers for the original problem from an effective 1D problem.

#### Yang Lei

**Title:** A voyage to non-AdS holography [video]

**Abstract:** AdS/CFT is the best studied example of holography. For practical use in condensed matter theory, and also for theoretical interests, it is necessary to develop the theory of non-relativistic holography. One may ask the question: how general the idea of holography can be? In this talk, I will provide examples of non-relativistic holography by using 3D Chern-Simons theory. I will show some features of holography can exist even in the non-relativistic limit of AdS3/CFT2.

#### Shiraz Minwalla

**Title:** Regular boson-critical fermion Chern-Simons duality [video]

**Abstract:** It is now well established that Chern Simons gauged Critical Bosons are level rank dual to Chern Simons gauged regular fermions. It has also been suggested that there is a sense in which CS gauged regular fermions are dual to CS gauged critical bosons. In this talk we study these two theories in detail in the large $N$ limit. Our results suggest a sharp duality conjecture between these two theories.

#### João Rodrigues

**Title:** Bilocals at the infrared fixed point of the three dimensional O(N) invariant vector theory with a quartic interaction [video]

**Abstract:** TBA

#### Rodolfo Russo

**Title:** CFT2 4-point correlators from classical geometries [video (truncated)]

**Abstract:** The AdS/CFT duality maps supersymmetric heavy operators with conformal dimension of the order of the central charge to asymptotically AdS supergravity solutions. I’ll show how by studying the quadratic fluctuations around such backgrounds it is possible to derive the 4-point correlators of two light and two heavy states in the supergravity approximation. I’ll present some explicit examples in the AdS3 setup relevant for the duality with the D1-D5 CFT and discuss what we can learn in general about correlators among (heavy) pure states.

#### Jaco van Zyl

**Title:** On Integrable subsectors of AdS/CFT and LLM geometries[video]

**Abstract:** The 1/2 BPS and regular LLM geometries are the result of a large number of D-branes backreacting on the AdS_5 x S^5 and are thus dual to operators that lie outside of the planar sector. Explicitly these operators are Schur polynomials built from a single complex scalar field and labelled by a Young diagram with O(N^2) boxes. In the Schur polynomial language one may add excitations to this configuration by simply adding additional boxes to the Young diagram. When excitations are restricted to a single, distant corner of the diagram there is a remarkable simplification that occurs in the large N limit - excitations only mix with other fields located at the same corner. This gives rise to an emergent gauge theory that, according to a recent proposal, should have a planar limit that is isomorphic to planar N = 4 SYM and thus also integrable. The only observable change should be an O(1) rescaling of the t’Hooft coupling. If correct, the proposal thus provides significant insight into the non-planar sector and provides an interesting new setting in which to develop the framework of integrability. In this talk the proposal is reviewed and aspects of the available weak and strong coupling evidence presented.

#### Alberto Zaffaroni

**Title:** Topologically twisted indices and holography [video]

**Abstract:** We define indices for topologically twisted supersymmetric theories from two to five dimensions. We apply them to the holographic study of AdS black holes, black strings and domain-walls across dimensions.

#### Costas Zoubos

**Title:** Marginal deformations and quasi-Hopf algebras [video]

**Abstract:** We elucidate the quasi-Hopf structure of the Leigh-Strassler N=1 superconformal marginal deformations of the N=4 Super-Yang-Mills theory. The R-matrix of these theories, which is related to the one-loop spin chain Hamiltonian in the scalar sector, does not generically satisfy the Quantum Yang-Baxter Equation. By constructing a Drinfeld twist which relates this R-matrix to the trivial R-matrix of the N=4 theory, and using that twist to construct a non-trivial co-associator, we show that the generic Leigh-Strassler R-matrix satisfies the quasi-Hopf version of the QYBE. We also use the twist to define a suitable star product which directly relates the N=4 SYM superpotential to that of the marginally deformed gauge theories. We expect our results to be relevant to studies of integrability in these theories, as well as to provide useful input for supergravity solution-generating techniques.