Higher order corrections in the 1/N expansion to scattering amplitudes come from the diagrams with higher genus. One way to address these non-trivial topologies is to view them as planar objects glued into non-planar configurations. They can then be "cut" across all the cycles of the corresponding Riemann surface, fixing the momentum flowing in each cycle. This procedure results in a planar object that belongs to a representation of the modular group of the Riemann surface in question. Various techniques developed for the planar amplitudes can be generalized to these cut non-planar ones. We will investigate the scattering amplitude — Wilson loop duality, specifically focusing on the case of the first non-planar correction, 1/N double trace amplitude, which has the topology of a cylinder. It’s dual space interpretation is a correlator of two infinite Wilson lines subject to a periodicity constraint. We will confirm this duality by a weak coupling perturbative calculation and a strong coupling string worldsheet one. This will allow us to construct the non-planar loop integrands and the BCFW recursion relation they satisfy, as well as to find an interpretation of the dual conformal symmetry in the non-planar sector, which was previously thought to be broken by 1/N corrections. Lastly, we will discuss this result in the framework of the Wilson Loop OPE approach, which allows one to compute expectation values of Wilson loops at any value of the coupling in the form of an expansion around the collinear limit. We claim that this approach can be directly applied to cut non-planar scattering amplitudes, as well as the N=4 SYM form factors, whose dual space interpretation is remarkably similar to the one of the 1/N amplitude correction.

We overview some aspects of asymptotically de Sitter spacetimes at the classical and quantum level. We discuss some features of the late time de Sitter wavefunction. We briefly touch upon some properties of the relation between de Sitter space and Euclidean conformal theories, broadly referred to as the dS/CFT correspondence. Finally, time permitting, we will discuss some similarities and differences between the cosmological dS horizon and a more standard black hole horizon.

I will first review the AdS4/SCFT3 correspondence with N=4 supersymmetry. I will then focus on two special aspects which are important in exploring the string landscape: (1) The existence of N=2 moduli and their fate in gauged supergravity; (2) Special degeneration limits for which the low-energy limit is a theory of bigravity or massive gravity.

Disconnected gauge groups have been, at least comparatively, very poorly studied. Yet they may hide very interesting Physics. Recently, a class of gauge theories based on a particular type of disconnected gauge groups, namely principal extensions, has been introduced. Interestingly, such theories naturally implement the gauging of charge conjugation. In this talk, we will describe such construction and study aspects of its Physics. A particularly spectacular by-product of the construction is that these theories have non-freely generated Coulomb branches, thus providing the first counterexample of the long standing standard lore that Coulomb branch are all freely generated.

Chern-Simons theories coupled to fundamental matter have a wide variety of applications ranging from Quantum Hall effect to Quantum gravity via AdS/CFT. These theories enjoy a strong weak duality that has been tested to a very good accuracy via large N computations, such as thermal partition functions, and S matrices. Supersymmetric Chern-Simons theories are equally interesting since they have a self duality and relate to non-supersymmetric theories via RG flows. In the N=2,3 supersymmetric Chern-Simons matter theories, the four point amplitude computed to all orders in the 't Hooft coupling is not renormalised! It is a unique situation in a quantum field theory that the scattering amplitude doesn't receive loop corrections. This indicates the presence of powerful symmetry structures within the theory. This also suggests that higher point amplitudes may be easier to compute using four point amplitudes as building blocks. These higher point amplitudes not only serve as a testing tool for duality but also a probe into the symmetry structure of the theory. As a first step towards this goal, we begin by computing arbitrary n point tree level amplitudes in the N=2 theory via BCFW recursion relations. We then show that the four point tree level amplitude enjoys a dual superconformal symmetry. Since the all loop four point amplitude is tree level exact, it follows that the dual superconformal symmetry is exact to all loops. This is in contrast to highly supersymmetric examples such as N=4 SYM and N=6 ABJM, where the dual superconformal symmetry is in general anomalous. Furthermore, we show that the superconformal and dual superconformal symmetries generate an infinite dimensional Yangian symmetry for the four point amplitude. If these symmetries persist to higher point amplitudes, this suggests that the N=2 superconformal Chern-Simons matter theory may be integrable.

What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider the spatial entanglement between two intervals in the Gross-Taylor model, the string theory dual to two-dimensional Yang-Mills theory at large N. The string diagrams that contribute to the entanglement entropy describe open strings with endpoints anchored to the entangling surface, as first argued by Susskind. We develop a canonical theory of these open strings, and describe how closed strings are divided into open strings at the level of the Hilbert space. We derive the Modular hamiltonian for the Hartle-Hawking state and show that the corresponding reduced density matrix describes a thermal ensemble of open strings ending on an object at the entangling surface that we call an E-brane.

M-theory is a candidate for a theory of quantum gravity. Its fundamental objects are called M2-branes and M5-branes. The low-energy theory describing coincident M5-branes is poorly understood in many respects, with holography providing one of the most useful tools to further that understanding. It is known that the theory should possess solitonic solutions called "self-dual strings". An important quantity characterising these strings is their central charge, which among other things counts the massless degrees of freedom on the string. I will describe configurations of M-branes dual to the insertion of infinite tension self-dual strings into the M5-brane theory, and how calculation of holographic entanglement entropy in such set-ups yields the central charge of the self-dual string.

String theory predicts its own gravity rather than GR. In General Relativity the metric is the only geometric and gravitational field, whereas in string theory the closed-string massless sector comprises a skew-symmetric B-field and the string dilaton in addition to the metric. Furthermore, these three fields transform into each other under T-duality. This hints at a natural augmentation of GR: upon treating the whole closed string massless sector as stringy graviton fields, Double Field Theory may evolve into `Stringy Gravity'. Equipped with an O(D,D) covariant differential geometry beyond Riemann, we spell out the definitions of the stringy Einstein curvature tensor and the stringy Energy-Momentum tensor. Equating them, all the equations of motion of the closed string massless sector are unified into a single expression which we dub the Einstein Double Field Equations.

A review of the recent progress regarding the holograhic duals for viscoelastic and solid materials. After introducing a simple bottom-up model able of realizing such a setup the following physical properties will be discussed: i) the linear elastic features ii) viscoelasticity ii) the nature of phonons and pinning iii) the non linear elastic properties iiii) the convergence properties of the asymptotic expansion.

Any sequence of quantum gates on a set of qubits defines a multipartite unitary transformation. These sequences may correspond to some parts of a quantum computation or they may be used to encode classical/quantum information (e.g. in private quantum channels). If we have only limited access to such a unitary transformation, we may want to store it into a quantum memory and later perfectly retrieve it. Thus, once we cannot use the unitary transformation directly anymore, we could still apply it to any state with the help of the footprint kept in the quantum memory. This can be useful for speeding up some calculations or as an attack for process based quantum key distribution protocol or a communication scheme. We require the storing and retrieving protocol to perfectly reconstruct the unitary transformation, which implies non unit probability of success. We derive optimal probability of success for a d-dimensional unitary transformation used N-times. The optimal probability of success has a very simple form N/(N-1+d^2). This result implies that reliable storing of d^2 parameters of the unknown unitary transformation requires roughly d^2 uses of the transformation.

I will summarise old and recent developments on the classification and solution of Rational Conformal Field Theories in 2 dimensions using the method of Modular Differential Equations. Novel and exotic theories are found with small numbers of characters and simple fusion rules, one of these being the Baby Monster CFT. Correlation functions for many of these theories can be computed using crossing-symmetric differential equations.

I will review how the requirements of unitarity, locality, causality and Lorentz invariance impose constraints on the signs of the operator coefficients in an effective field theory, discuss recent work on generalizing these constraints to arbitrary spin particles, and discuss how these can be used to constrain gravitational EFTs of the type considered by cosmologists as models for dark energy or inflation.

Non-Abelian T-duality, a transformation in String Theory known since the 90’s, has been shown recently to be a powerful solution generating technique in supergravity. In this talk I will discuss various AdS backgrounds generated through this transformation, for which it is possible to give a dual CFT interpretation arising from Hanany-Witten brane set-ups.

The computation of Feynman integrals is an important ingredient to compute scattering amplitudes to higher orders in perturbative QFT. Over the last couple of years, a lot of progress was made in understanding the mathematics of multi-loop Feynman integrals. In particular, it was understood that large classes of integrals evaluate to a class of special functions called multiple polylogarithms, which are an object of active research also in pure mathematics. It is known that starting from two loop, generalisations of polylogarithms to elliptic curves can show up. In this talk we review certain classes of elliptic multiple polylogarithms, and we show that they are closely related to iterated integrals on certain modular curves.

I present recent progress towards determining the planar S-matrix of maximally supersymmetric Yang-Mills theory, thanks to the rich interplay between its perturbative analytic properties in general kinematics, and its integrable structure in special kinematics. The former are related to cluster algebras, and allow for the computation of amplitudes with six/seven gluons up to six/four loops, whereas the latter yields all amplitudes in the multi-Regge limit at finite coupling.

Feynman diagrams will be looked at from a new point of view. 'Symmetries of Feynman Integrals' is an analytical method for calculating Feynman diagrams. It is based on exposing an underlying group structure of a given diagram which defines a set of partial differential equations in the parameter space of the diagram. Group orbits in the diagram’s parameter space are used to reduce the Feynman integral into a line integral. The vacuum seagull, a three-loop diagram, and the propagator seagull, a propagator-type diagram with two loops, will be used to demonstrate the method, and to obtain new results.

TBA

The scaling behavior near the transition between plateaus of the integer quantum Hall effect has traditionally been interpreted on the basis of a two-parameter renormalization group flow conjectured from the non-linear sigma model of Pruisken. Yet, this scaling picture never led to any analytical understanding of the critical point. Here we propose a novel description of the critical point as Pruisken's nonlinear sigma model coupled to a maximally gauged Wess-Zumino-Witten model of level 4. This proposal explains the existing numerical data for the multifractal scaling exponents of critical wavefunctions.