The monodromy relations of scattering amplitudes in string theory provide an elegant formalism to understand some mysterious properties of tree-level field theory amplitudes, like the color-kinematics duality. This duality has been instrumental in tremendous progress on the computations of loop-amplitudes in quantum field theory, but a loop-level generalisation of the stringy monodromy construction has been lacking for many years. In this talk I will first describe some of these recent developments in the domain of scattering amplitudes in gauge and gravity theories. I’ll then review the monodromies of open string worldsheets and how the lead at tree-level to deepening the understanding of the gauge theory perturbative expansion. Then I will describe in a non-technical manner our results and how we managed to extend these relations to all loops in string and field theory. I’ll finish by discussing implications for the loop expansion in general, and how to extend in principle these results to gravity. I will assume no prior knowledge of the audience in modern scattering amplitudes methods.

Models with spontaneously broken local supersymmetry are naturally obtained by coupling the off-shell supergravity-matter systems to Goldstino superfields. Every irreducible Goldstino superfield produces a universal positive contribution to the cosmological constant. This talk will review the structure of N=1 and N=2 Goldstino superfields.

In this talk I will discuss recent developments that have suggested new connections between the transport properties of strongly interacting matter and the field of quantum chaos. In particular I will describe how in many holographic theories there are simple relationships between the thermoelectric diffusion constants and the butterfly velocity, which describes the speed at which quantum chaos propagates.

TBA

I will discuss some aspects of the doubled geometry of double field theory. Double field theory provides a reformulation of supergravity with a manifest O(D,D) symmetry, which can be related to the T-duality invariance of string theory on a torus. I will review how one achieves this, by doubling the number of coordinates and introducing a generalised diffeomorphism symmetry. Then, I will discuss how one can characterise the properties of string theory backgrounds viewed as solutions of DFT, and in particular show how to derive the first law of black hole thermodynamics in this framework. Based mainly on 1507.07541 and 1608.04734 (with Alex Arvanitakis).

Compactifications of M-theory down to AdS4 are known to arise from Sasaki-Einstein internal spaces. The latter can be viewed as surfaces enclosing Calabi-Yau cone singularities, whose deformations can be described algebraically in a well established way. In this talk, I will present work in progress on describing deformations of the enclosing surfaces away from the Sasaki-Einstein metric, using the deformations of the Calabi-Yau cone. This provides a realisation of a class of SU(3) structure manifolds satisfying the conditions postulated in the standard treatments of M-theory compactifications on such manifolds. The result is a proposal for obtaining four dimensional N=2 supergravity models with gauged hypermultiplets from deformations of regular Sasaki-Einstein manifolds.

Recent work has uncovered relations between the rate at which chaotic behaviour spreads in strongly interacting quantum systems, and the diffusivities of certain processes in these systems. Focusing mainly on holographic examples, I will explore the extent to which these relations hold in states at non-zero density, where the diffusion of charge and energy are no longer independent processes.

A microstate geometry is a smooth, time-independent, asymptotically flat, horizon-free solution of type IIB supergravity. According to the “fuzzball" conjecture, such solutions describe individual microstates of black holes. Non-supersymmetric microstate geometries typically suffer from linearized instabilities. I will argue that supersymmetric microstate geometries suffer from a nonlinear instability. I will also discuss how such solutions lead to a new type of mathematical structure, so-called “ambipolar” hyperkahler manifolds, and explain how such manifolds can be constructed.

The appearance of integrability in the duality between the AdS5xS5 string and planar maximally supersymmetric Yang-Mills theory gives rise to many insightful results. Various deformations of this AdS/CFT dual pair are known to also be integrable, prompting the question how far the power of integrability extends in this setting. In recent years there has been a lot of progress in answering this question. Rather than trying to demonstrate integrability in known AdS/CFT dual pairs, efforts instead focused on finding manifestly integrability preserving deformations of the AdS5xS5 string. While constructed to preserve integrability, the resulting so-called Yang-Baxter sigma models are, however, not guaranteed to describe strings, or have an AdS/CFT interpretation. The former of these points has since been addressed and turns out to be closely related to (nonabelian) T duality, and we now understand which of these models continue to describe strings. The goal of my talk is to address the latter point, regarding the AdS/CFT interpretation of these models. I will use symmetry considerations to give a unified AdS/CFT picture for these Yang-Baxter strings as duals to various noncommutative deformations of supersymmetric Yang-Mills theory. My general conjecture matches many known dualities, and I will briefly discuss nontrivial tests in various new cases, in the form of brane constructions indicating the desired dualities.

The a-theorem expressing the monotonicity of renormalisation group flows in four (and other even) dimensions is now well-accepted. There is a function (the a-function) generating the RG beta-functions as a gradient flow via a positive-definite metric. However the standard definition of the a-function in terms of the trace anomaly of the energy-momentum tensor does not work in odd dimensions. In this talk we focus on the gradient-flow property of the a-function and show that a function with similar properties can be constructed order-by-order in three dimensions. We start by reviewing the a-function in even dimensions from a gradient-flow standpoint. Then we discuss our explicit calculations in three dimensions. Finally we present some progress towards relating our results to the F-function which has been shown to have the expected monotonicity properties at fixed points.

Recent advances in non-geometric string theory suggest that locally non-geometric flux compactifications can be understood in terms of nonassociative deformations of spacetime geometry. We will review some of these developments and how they shed light on properties of non-geometric strings, and explain some new results concerning how these structures lift to non-geometric M-theory.

In this talk, I will discuss how the two geometric notions "fan" and "monoid" can be very fruitful for the understanding of the monopole formula for 3d N=4 gauge theories. After a brief reminder of the monopole formula, I will introduce the matter fan and reorganise the monopole formula accordingly. I then discuss the resulting benefits such as: (1) Explicit expressions for the Hilbert series built from well-studied constituents. (2) Proof that the order of the pole at t=1 and t → ∞ equals the complex or quaternionic dimension of the Coulomb branch. (3) Identification of a sufficient set of chiral ring generators.

I am going to talk about how to derive an exact partition function of supersymmetric field theories on a supersymmetry-preserving quotient of Euclidean AdS_3 by localization. This is one of first examples about localization on non-compact spaces. I will describe the situation by comparing it to a situation in compact spaces. Then, I will explain how to perform a localization procedure on the manifold, and finally, I will discuss the features of the partition function we derived.

I review the theory of non-linear realisations and Kac-Moody algebras, I explain how to construct the non-linear realisation based on the Kac-Moody algebra $E_{11}$ and its vector representation. I explain how this field theory leads to dynamical equations which contain an infinite number of fields defined on a spacetime with an infinite number of coordinates. I then show that these unique dynamical equations, when truncated to low level fields and the usual coordinates of spacetime, lead to precisely the equations of motion of eleven dimensional supergravity theory. By taking different group decompositions of $E_{11}$ we find all the maximal supergravity theories, including the gauged maximal supergravities, and as a result the non-linear realisation is a unified theory that is the low energy effective action for type II strings and branes. These results essentially confirm the $E_{11}$ conjecture given many years ago.

Weyl semi-metals are an exciting new class of 3D materials with exotic transport properties. They are characterised by point like singularities in the Brillouin zone at which conduction and valence bands touch. Around these points the electronic quasi-particle excitations can be described by either left- or right-handed Weyl spinors. This makes high energy physics to be the low energy electronics of these materials. Holographic models might be useful in two ways: first some Weyl semi-metals might be strongly interacting and second holography is our best tool to understand and discover new exotic transport properties related to the chiral nature of the charge carriers, especially to chiral anomalies. I will review the construction of a holographic model supporting a topological quantum phase transition between a topological Weyl semi-metal phase and a trivial phase and use it to predict the existence of a new dissipation less form of viscosity (Hall viscosity) in the quantum critical region.

In a generic CFT the spectrum of operators carrying a large U(1) charge can be analyzed semiclassically in an expansion in inverse powers of the charge. The key is the operator state correspondence by which such operators are associated with a finite density superfluid phase for the theory quantized on the cylinder. The dynamics is dominated by the corresponding Goldstone hydrodynamic mode and the derivative expansion coincides with the inverse charge expansion. I will illustrate this situation by first considering simple quantum mechanical analogues and then will systematize the approach by employing the coset construction for non-linearly realized space-time symmetries. Focussing on CFT3 I will illustrate that the three point function coefficients turn out to satisfy universal scaling laws and correlations as the charge and spin are varied.

We numerically construct asymptotically global AdS_5 x S^5 black holes that are localised on the S^5. These are solutions to type IIB supergravity with S^8 horizon topology that dominate the microcanonical ensemble at small energies. At higher energies, there is a first-order phase transition to AdS_5-Schwarzschild x S^5. By the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, this transition is dual to spontaneously breaking the SO(6) R-symmetry of N=4 supersymmetric Yang-Mills down to SO(5). We extrapolate the location of this phase transition and compute the expectation value of a scalar operator in the low energy phase. In addition, we discuss the construction of localised black holes in type IIA, which are dual (via T-duality) to the low temperature phase of thermal 1+1 dimensional supersymmetric Yang-Mills theory on a circle.

We consider planar hairy black holes in five dimensions with a real scalar field in the Breitenlohner-Freedman window. We show that is possible to derive a universal formula for the speed of sound for any theory. As an example we find all the planar black holes of the single scalar field consistent truncation of type IIB that preserves the SO(3)×SO(3) R-symmetry group of the gauge theory. We find the speed of sound for different values of the induced vacuum expectation value when a double trace deformation is induced in the gauge theory. For any theory, we show that the speed of sound is not bounded by any special value.

The planar scattering amplitudes of 4d N = 4 super Yang-Mills theory and 3d N=6 Chern-Simons theory exhibit a remarkable property known as dual conformal symmetry. Motivated by this, we investigate the consequences of dual conformal symmetry in six dimensions. We find that 6d dual conformal symmetry fixes the structure of the one-loop 4-point amplitude and suggests a Lagrangian with more than two derivatives. Moreover, we obtain a similar structure by generalizing the Alday-Maldacena solution for a string in Anti-de Sitter space to a 2-brane ending on a pillow-shaped surface in the boundary whose seams correspond to a null-polygon, which suggests an all-loop formula for the 4-point amplitude similar to that of N=4 super Yang-Mills theory.

I’ll review old and new aspects of deformed instanton equations derived from D-branes.