Polygon Seminar. NOTE: Seminar is in the room G.73, Franklin-Wilkins, WATERLOO CAMPUS of King's College London. http://www.kcl.ac.uk/campuslife/campuses/waterloo/Waterloo.aspx

I consider the the effect of weak integrability breaking interactions on the non-equilibrium time evolution in many-particle systems. Using a class of weakly interaction fermion models as an example, I argue that there exists a time window in which the system relaxes locally to a non-equilibrium meta-stable state, before it eventually thermalizes.

I discuss general properties of supersymmetric Anti-de Sitter (AdS) backgrounds, in particular regarding their moduli spaces and domain walls. I argue that lower-dimensional gauged supergravity is a strong tool to understand supersymmetric AdS backgrounds, independent of the compactification manifold. I show how the moduli space can be determined and explain what this means for the dual conformal field theories. In the last part I comment on supersymmetric domain walls and their dual interpretation as supersymmetric RG- flows.

We propose a new strategy to constraint (and perhaps determine) the mass spectrum and the scattering amplitudes of a Quantum Field Theory (QFT). We consider QFT in hyperbolic space and study correlation functions of operators inserted at the conformal boundary. By construction, these observables transform like correlation functions of a lower dimensional Conformal Field Theory. We then apply conformal bootstrap techniques to find universal bounds on the mass spectrum and scattering amplitudes of the QFT. For 1+1 dimensional QFT, we recover the same bounds from a direct S-matrix bootstrap approach.

I'll overview recent progress on non-perturbative aspects of higher spin theories in three dimensions with emphasis on black holes. The two main results I will discuss are: 1) novel properties of extremal and BPS solutions, and 2) how to interpret a higher spin bh as a thermo-field state.

In this talk, I will discuss Type IIA brane configurations consisting of D4-branes suspended between NS5-branes which represent a large class of 2d (0,2) quiver gauge theories. We call these new constructions Brane Brick models. These are T-dual to D1-branes over singular toric Calabi-Yau 4-folds and encode information about the probed Calabi-Yau geometry as well as the corresponding GLSM. If time permits, I will present how Brane Brick models naturally realise in terms of a brane configuration 2d (0,2) Gadde-Gukov-Putrov triality.

A major paradigm of 20th-century science is to understand nature in the language of quantum field theory. Efforts to answer foundational questions about this language have led to successful and ongoing cross-fertilisation between theoretical physics and pure mathematics. In particular, Atiyah and Segal proposed an axiomisation of the path integral by beautifully linking geometry with algebra. The talk starts with a lightening review of this functorial approach, and then quickly restricts to the case in which spacetime is two-dimensional and has no geometric structure: two-dimensional topological quantum field theory (TQFT). This seemingly simple situation is still surprisingly rich, and we will see how algebras, categories, and "higher" structures appear naturally; examples of such structures are ubiquitous in theoretical physics, string theory, and many areas of mathematics. Once the stage is carefully set, we turn to the central notion of symmetry, which involves the action of groups on a TQFT. We will be led to interpret symmetries as special kinds of "defects" of the TQFT, which in turn allows for a natural, purely algebraic generalisation of orbifolding. This leads to new equivalences between TQFTs, of which we will discuss the examples of Landau-Ginzburg models, and (if time permits) refined knot invariants.

The goal of this talk is to show some uses of the Gronewold-Moyal product in physics and new applications. In the first part of this talk we review the approach of Gronewold and Moyal in the quantization of classical systems. Then we remark algebraic aspects related to the representation of symplectic algebras and extensions of Anti-de-Sitter algebras. Subsequently we describe how these aspects are used in higher spin gravity. In the second part of this talk we present some new advances. We quantize a particular class of algebraic varieties, involving multivectors, and which contains Minkowski space slices. We show that these non-commutative geometries are solutions of known matrix models and some simple extensions of them. Then we present new models which describe the dynamics of extended objects in close resemblance to the equations of Hamiltonian systems. We also introduce statistical distributions in these spaces which encode their coordinates spectra.

I will present a framework for computing correlators of three single trace operators in planar N=4 SYM theory that uses hexagonal patches as building blocks. This approach allows one to exploit the integrability of the theory and derive all loop predictions for its structure constants. After presenting the main ideas and results, I will discuss recent perturbative tests and open problems.

In 2007, it was conjectured by E.Witten that the chiral part of the partition function of 3d pure AdS Einstein gravity in quantum regime coincides with so-called modular J-function, a partition function of certain holomorphic CFT, called "monster CFT" considered by I. B Frenkel, J. Lepowsky and A. Meurman in the context of monstrous moonshine. We tried to calculate the partition function for the 3d pure AdS Einstein gravity directly by utilizing recently developed localization techniques.Based on some plausible assumptions, we arrived at CFT interpretations.For quantum gravity regime which corresponds to c=24, we get J-function.For semiclassical regime which corresponds c>>1, our partition function decomposes to Virasoro characters, and we derive Cardy formula. If possible, I will comment on application to quantum higher spin gravity.This talk is based on 1504.05991 and 1510.02142.

I will describe recent progress in computing Weyl anomalies in strongly-coupled six-dimensional field theories. Along the way we will prove an a-theorem quantifying the loss of degrees of freedom along renormalization group flows.

One of the great successes of string theory, as a theory of quantum gravity, is the explanation of the entropy of asymptotically-flat black holes. I will present, instead, a counting of the microstates of certain black holes in AdS4. The black holes have an holographic description as RG flows from a 3D CFT to superconformal quantum mechanics, and the counting of microstates proceeds via supersymmetric localization. Along the way, we will define and compute an index for topologically twisted theories, and propose an extremization principle to determine the superconformal R-symmetry in quantum mechanics.

Two interesting properties of static curved space QFTs are Casimir Energies, and the Energy Gaps of fluctuations. We investigate what AdS/CFT has to say about these properties by examining holographic CFTs defined on curved but static spatially closed spacetimes. Being holographic, these CFTs have a dual gravitational description under Gauge/Gravity duality, and these properties of the CFT are reflected in the geometry of the dual bulk. We can turn this on its head and ask, what does the existence of the gravitational bulk dual imply about these properties of the CFTs? In this talk we will consider holographic CFTs where the dual vacuum state is described by pure Einstein gravity with negative cosmological constant. We will argue using the bulk geometry first, that if the CFT spacetime's spatial scalar curvature is positive there is a lower bound on the gap for scalar fluctuations, controlled by the minimum value of the boundary Ricci scalar. In fact, we will show that it is precisely the same bound as is satisfied by free scalar CFTs, suggesting that this bound might be something that applies more generally than just in a Holographic context. We will then show, in the case of 2+1 dimensional CFTs, that the Casimir energy is non-positive, and is in fact negative unless the CFT's scalar curvature is constant. In this case, there is no restriction on the boundary scalar curvature, and we can even allow singularities in the bulk, so long as they are 'good' singularities. If time permits, we will also describe some new results about the Hawking-Page transition in this context.

In this talk I will describe co-dimension 2 and 4 defects in 6d (2,0) theories in several points of view: 3d SL(N,C) Chern-Simons theory (state-integral model, cluster algebra), 3d N=2 field theory, 5d N=2 super Yang-Mills, and AdS4 holographic dual. This leads to quantitative consistency checks of different approaches, as well as new predictions for a variety of partition functions.

We numerically construct asymptotically anti-de Sitter (AdS) black holes in four dimensions that contain only a single Killing vector field. These solutions, which we coin black resonators, link the superradiant instability of Kerr-AdS to the nonlinear weakly turbulent instability of AdS by connecting the onset of the superradiance instability to smooth, horizonless geometries called geons. Furthermore, they demonstrate non-uniqueness of Kerr-AdS by sharing asymptotic charges. Where black resonators coexist with Kerr-AdS, we find that the black resonators have higher entropy. Nevertheless, we show that black resonators are unstable and comment on the implications for the endpoint of the superradiant instability.

Ambitwistor strings are holomorphic string theories whose target space is the space of complex null geoedesics in complexified space-times. I will explain how these theories explain the origin of the scattering equations in twistor strings and the CHY formulae in arbitrary dimensions and provide a reformulation of standard gauge, gravity and other theories in a holomorphic infinite tension analogue of conventional string theories. I will show how these results extend to 1-loop both on a torus and on a nodal Riemann sphere, and perhaps to higher loops.

In this talk I will consider brane configurations that include NS5 branes, orientifold planes and anti-branes. I will argue that the class of field theories that live on such brane configurations admit Seiberg duality. Interactions between branes and orientifold planes will be given a field theory interpretation. In particular a certain repulsive interaction will lead to a non-trivial Coleman-Weinberg potential and dynamical symmetry breaking. I will also discuss the case of type 0' strings and chiral symmetry breaking of the form SU(Nf)xSU(Nf)-->SU(Nf) in a QCD-like theory.

There exist, in d=2+1 dimensions, field theories that are supersymmetric but non-relativistic. I will show that the low-energy physics of these theories is that of the fractional quantum Hall effect. Supersymmetry provides enough analytic control to explicitly derive the ground state wavefunctions and their excitations.