In this talk, I will discuss about the holography of boundary Conformal Field theory. I will show how boundary Weyl Anomaly can be obtained from holography. New universal relations between the shape dependence of Casimir effects and boundary Weyl anomaly will also be pointed out and discussed from the point of view of holography.

The talk is based on a very recent work of the speaker on generalising Zamolodchikov's c-theorem to non-unitary theories.

I will give an introduction to current topics in the study of scattering amplitudes of gauge theory and gravity. There will be four two-hour lectures, and the plan is as follows. Lecture 1 will review basic modern techniques for scattering amplitudes, including recursion relations. Lecture 2 will present an overview of the relations describing gravity as a double copy of gauge theory, both for scattering amplitudes and for solutions to the equations of motion. Lecture 3 will introduce the formalism of the scattering equations, leading to the CHY formulas for amplitudes in theories of massless particles. Lecture 4 will present new developments in computing field-theory amplitudes from string-theory-inspired techniques, via a new type of worldsheet model known as ambitwistor string. This leads to an extension of the scattering equations to loop level.

I will give an introduction to current topics in the study of scattering amplitudes of gauge theory and gravity. There will be four two-hour lectures, and the plan is as follows. Lecture 1 will review basic modern techniques for scattering amplitudes, including recursion relations. Lecture 2 will present an overview of the relations describing gravity as a double copy of gauge theory, both for scattering amplitudes and for solutions to the equations of motion. Lecture 3 will introduce the formalism of the scattering equations, leading to the CHY formulas for amplitudes in theories of massless particles. Lecture 4 will present new developments in computing field-theory amplitudes from string-theory-inspired techniques, via a new type of worldsheet model known as ambitwistor string. This leads to an extension of the scattering equations to loop level.

I will give an introduction to current topics in the study of scattering amplitudes of gauge theory and gravity. There will be four two-hour lectures, and the plan is as follows. Lecture 1 will review basic modern techniques for scattering amplitudes, including recursion relations. Lecture 2 will present an overview of the relations describing gravity as a double copy of gauge theory, both for scattering amplitudes and for solutions to the equations of motion. Lecture 3 will introduce the formalism of the scattering equations, leading to the CHY formulas for amplitudes in theories of massless particles. Lecture 4 will present new developments in computing field-theory amplitudes from string-theory-inspired techniques, via a new type of worldsheet model known as ambitwistor string. This leads to an extension of the scattering equations to loop level.

I will give an introduction to current topics in the study of scattering amplitudes of gauge theory and gravity. There will be four two-hour lectures, and the plan is as follows: Lecture 1 will review basic modern techniques for scattering amplitudes, including recursion relations. Lecture 2 will present an overview of the relations describing gravity as a double copy of gauge theory, both for scattering amplitudes and for solutions to the equations of motion. Lecture 3 will introduce the formalism of the scattering equations, leading to the CHY formulas for amplitudes in theories of massless particles. Lecture 4 will present new developments in computing field-theory amplitudes from string-theory-inspired techniques, via a new type of worldsheet model known as ambitwistor string. This leads to an extension of the scattering equations to loop level.

In this talk we will discuss how gauge invariance fixes the soft behavior of massless particles as photons, gluons, gravitons, dilatons and Kalb-Ramond field. We will then check these results in string theory and we will show that the subsubleading behavior for gravitons includes string corrections in the bosonic and heterotic strings, but not in superstring. They are consequence of the fact that the three-graviton amplitude has string corrections with respect to the field theoretical one. It turns out, instead, that the soft behavior of the dilaton has no string corrections and, in particular, involves the generators of dilatations and special conformal transformations. We then study the soft behavior of the Goldstone boson, called in the literature also dilaton, that one gets when one breaks spontaneously the conformal symmetry and we show that its soft behavior is very similar, but not identical, to that of the string dilaton.

We will introduce a large class of N=1 superconformal theories Sk which is obtained from Gaiotto’s N=2 class S via orbifolding. We will study the Coulomb branch of the theories in the class by constructing and analyzing their spectral curves. Using our experience from the N=2 AGT correspondence we will search for a 2D/4D relations (AGTk) for the N=1 theories of class Sk. From the curves we will identify the 2D CFT symmetry algebra and its representations, namely the conformal blocks of the Virasoro/W-algebra, that underlie the 2D theory and reproduce the Seiberg-Witten curves of the N = 1 gauge theories. We find that the blocks corresponding to the SU(N) Sk gauge theories involve fields in certain non-unitary representations of the WkN algebra. These conformal blocks give a prediction for the instanton partition functions of the 4D N = 1 SCFTs of class Sk.

The nature of the unknown non-baryonic energy density component whose abundance is known to exceed the amount of ordinary, visible matter by a factor of five, that of Dark Matter (DM), is one of the greatest open problems in cosmology. In this talk I will briefly review the evidence and searches for DM, present an overview of candidates including the standard WIMP paradigm, and discuss some recently proposed alternatives for WIMPs and how to test them.

String theory in the tensionless limit is expected to have a large gauge symmetry. By recasting string theory on the AdS background as a generalization of Vasiliev's theory of massless higher-spin fields, it has become possible to understand the nature of this symmetry. In this talk, I will first give an overview of three-dimensional Vasiliev theory and its dual CFT. I will then discuss the current understanding of the symmetry algebra of string theory as well as some open problems related to it.

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

This talk will focus on some recent results concerning the low energy expansion of superstring scattering amplitudes. Whereas tree-level amplitudes generate a series of multiple zeta values (MZV) the genus-one amplitudes generate a series of elliptic generalisations (“modular graph functions”) that satisfy fascinating polynomial relations analogous to those satisfied by MZV’s. The latter part of the talk will briefly review how these features fit in with the non-perturbative structure of superstring amplitudes, studied some time ago.

This talk is about integrability of Planar N=4 super Yang-Mills theory. We present a concrete notion of the corresponding Yangian symmetry in this model, show that it holds true, and discuss the (perturbative) implications for correlation functions and Wilson loops.

It has been known since the 80's that the Green-Schwarz superstring possesses the fermionic kappa symmetry, required for the consistency of the formulation, if the target space is a solution of the supergravity equations of motion. However, contrary to the standard lore and previous claims in the literature, it was recently shown that the converse is not true. Kappa symmetry of the Green-Schwarz superstring implies only a weaker set of equations for the target space fields, which we refer to as generalized supergravity equations. I will describe these equations for the type II case and contrast them with the standard type II supergravity equations which arise as a special case.

I present the results of a study of a (1 +1 )-dimensional version of the famous Nambu-Jona-Lasinio model of quantum chromodynamics both at zero and at finite baryon density. For zero chemical potential, we found the formation of fermionic (nucleons and Δ baryons) and bosonic (two-quark mesons, six-quark deuterons) excitations, and demonstrated the existence of a phase transition. For a finite baryon density the model has a rich phase diagram which includes phases with a density wave and superfluid quasi-long-range (QLR) order, as well as a phase of a baryon Tomonaga-Luttinger liquid (strange metal). Relevant publication: P. Azaria, R.M. Konik, Ph. Lecheminant, T. Pálmai, G. Takács and A.M. Tsvelik: Particle Formation and Ordering in Strongly Correlated Fermionic Systems: Solving a Model of Quantum Chromodynamics, Phys. Rev. D94 (2016) 045003, arXiv:1601.02979 [hep-th].

An early epoch of cosmic inflation, driven by a scalar field slowly rolling down a flat potential, provides an elegant solution to several cosmological puzzles. The notorious sensitivity of the slow roll potential to quantum gravity effects, presents both a challenge and opportunity for string theory to connect to observations. A very promising way to explain slow roll inflation is with an axionic inflaton field, whose flat potential is protected by a perturbative shift symmetry. However, the canonical models of axion inflation - "Natural Inflation" and "Axion Monodromy" - are now both in tension with observations and difficult to embed in a UV complete theory like string theory. I will discuss these challenges, and also a way to overcome them, with an inflationary mechanism - beyond slow roll - that is well-motivated from string theory and consistent with observations, including distinctive signatures to be searched for in future observations.

We compute the holographic entanglement entropy for the pure gravitational anomaly in 3+1 dimensions. Using the perturbative method developed for com- puting entanglement entropy for quantum field theories, we also compute the parity odd contribution to the entanglement entropy of the dual field theory that comes from a background gravitational Chern-Simons term. We find that, in leading order in the perturbation of the background geometry, the two contribu- tions match except for a logarithmic divergent term on the field theory side. We interpret this extra contribution as encoding our ignorance of the source which creates the perturbation of the geometry.

Poincaré invariance imposes strong non-perturbative constraints on the dependence of scattering amplitudes on the kinematical variables. For massless external states, Benincasa and Cachazo have shown that the 3-point amplitude is fully determined up to a constant (the coupling). We extend their approach, based on the spinor-helicity formalism, to time-like momenta, and we find that, even when massive external states are involved, the functional form of the 3-point amplitude is fully determined, up to (several) constants. In this talk I review the derivation in the massless case, enlightening the role of the little group covariance of the amplitude in constraining its functional form, and the particularly simple form that these constraints get in the spinor language. Then I will show how to extend this procedure to the massive case, deriving the constraining equations for the massive little group, and eventually showing the expressions for 3-point amplitudes involving one, two, or three massive particles.