LUSO-BRAZILIAN MEETING
IN
THEORETICAL AND MATHEMATICAL PHYSICS

ABSTRACTS

Speaker: P. Vieira

An introduction to Integrability in AdS/CFT

Abstract:  

TBD

Speaker: T. Fleury

Aspects of Superstrings in AdS5 x S5

Abstract:

In this lecture, I will begin by reviewing some calculations using the AdS5 x S5 superstring action. Additionally, I will address several open problems. The pure spinor formalism will play a crucial role and will be both utilized and defined. I will discuss the integrability of the model. The Lax pair of this model is given in terms of the left invariant currents and ghosts. I will explain the importance of understanding the current algebra for accessing the spectrum. Finally, I will comment on the quantum corrections and vertex operators.

Speaker: G. Ruzza

On the spectral problem of Buryak-Rossi quantum KdV hierarchy

Abstract:  

The main part of this talk will be an overview of the construction (due to Buryak and Rossi) of quantum integrable hierarchies from the geometry of the moduli spaces of curves. The simplest example of this construction realizes explicitly a quantization of the classical integrable hierarchy of evolutionary symmetries of the KdV equation (quantized with respect to the so-called first Poisson structure). Finally, I will report on ongoing progresses in the study of the spectrum of such quantum KdV hierarchy. 

Speaker: G. Degano

WKB analysis of anharmonic oscillators - A case study

Abstract:

Spectral problems associated with Schroedinger operators whose potential V (x) behaves as V (x) ∼ x2α, x → ∞, α > 0, and V (x) ∼ ℓ(ℓ+1)x−2, x → 0, have being subject to much attention since the beginning of quantum mechanics. In the late nineties, there was a renewed interest in such potentials due to the discovery of a link between them and integrable models in statistical and quantum conformal field theories, that has been called ODE/IM correspondence (P. Dorey, R. Tateo (1998) and V. Bazhanov, S. Lukyanov, B. Zamolodchikov (2001)). Motivated by the ODE/IM correspondence for the quantum KdV model, in this talk we describe the relevant spectral problems in the complex domain for a Schroedinger operator with potential V (x) = x2α+ℓ(ℓ+1)x−2−E, and we study it via the complex WKB method. In particular we describe the asymptotics of the spectrum in various asymptotic regimes of the parameters, for example the large energy limit E → ∞, the semiclassical limit E, ℓ → ∞, and the infinite degree of anharmonicity limit α → +∞.

Speaker: A. Retore

New (and not so new) integrable spin chains 

Abstract: 

Solving strongly interacting models can be a highly nontrivial task since perturbation theory is not applicable at large coupling. Luckily, there exists a class of models which can be solved even for very large coupling constants; they are called integrable models and have been playing an important role in modern theoretical physics: both in high-energy physics and condensed matter.

Integrable models are characterised by the presence of a huge amount of hidden symmetries, have beautiful algebraic structures, and more importantly, several techniques can be applied to solve them. Nonetheless, it was in general very difficult to discover if a model is integrable or not and to systematically construct new integrable models. We made progress in this direction and showing a way to do this will be the main focus of the second part of this talk. But before that, in the first part we will give a pedagogical introduction to a type of integrable models known as integrable spin chains, whose interesting applications motivate the second part of this talk.

Speaker: J. Doucot

Fourier transform of Stokes data of irregular connections

Abstract: 

Moduli spaces of meromorphic connections with irregular singularities on curves can be seen, via the Riemann-Hilbert-Birkhoff correspondence, as moduli spaces of generalised monodromy data (or Stokes data), known as wild character varieties. When considered in families, they give rise to isomonodromy systems, which notably include the Painlevé equations.  A remarkable fact is that moduli spaces arising from connections with different ranks, numbers of singularities and pole orders, may be isomorphic. This is reflected in the corresponding isomonodromy systems by the fact that many Painlevé-type equations admit several Lax representations. Many of such isomorphisms are induced by the Fourier-Laplace transform. In this talk, I will discuss some invariants of moduli spaces of connections under the Fourier transform, as well as how to obtain in some cases explicitly the isomorphisms of wild character varieties corresponding to the transformation of Stokes data it induces. This is joint work with Andreas Hohl.

Speaker: I. Kostov

The gravitational six-vertex model: domain-wall boundary conditions

Abstract:  

The six-vertex model on a square lattice is the simplest two-dimensional statistical model with a line of critical points with continuously varying critical exponents. Its Hamiltonian description is given by the XXZ spin chain. Of particular interest are the observables involving domain-wall boundary conditions which appear as building blocks for some correlation function in integrable models. Here I will give a review of some old and new results on the six-vertex model a random lattice obtained by gluing squares together in all possible ways. This  system represents a  solvable discrete model of 2d quantum gravity. Its continuum limit is that of a one-dimensional string theory compactified on a circle  of length beta determined by the six-vertex weights. I will mainly focus on the 6v  NxN matrix model (MM) to whom  this string theory is the holographic dual. The 6v matrix model contains two free parameters: the compactification length beta and the ``cosmological constant'' kappa coupled to the size of the lattice. The partition function of the 6v MM  is a tau sinh-Gordon integrable hierarchy.  The  large-N limit is described by a spectral curve for which an analytic expression is obtained in terms of theta functions. I will show how the spectral curve can be used to compute disk partition functions with domain-wall boundary conditions. A joint work in progress with Andre Alves. 

Speaker: F. Aprile

Flying in the face of AdS5 x S5 SUGRA at one loop

Abstract: I will describe recent computations of four-point single particle correlators in type-IIB supergravity at one-loop in Newton’s constant.  These can be bootstrapped from tree level data and few crucial considerations about the spectrum of N=4 SYM. Then, I will show how a novel mechanism of pole cancellations in Mellin space fixes the difficult part of the result almost without effort.

Speaker: A. Guerrieri

Precision physics from Bootstrap: QCD spectrum from pion-pion scattering

Abstract:  

The S matrix Bootstrap aims at establishing universal bounds on physical observables using general principles. In this talk I will twist this logic and feed experimental data into the bootstrap to use it as a tool to perform rigorous analytic continuation of scattering amplitudes and learn the nonperturbative QCD physics. In doing so, I will review the assumptions and the algorithms we use to perform these numerical explorations.

Speaker: A. Mohammadi

Spectral walls in soliton collisions

Abstract: 

A spectral wall is an obstacle in the dynamics of a bosonic soliton. It involves the formation of an arbitrary long-living stationary state due to the transition of a normal mode into the continuum spectrum. It appears when coupling the original bosonic model to other fields like other bosons, impurities, or fermions. This spectral wall can be experienced if the boson or fermion field is in an excited state. A spectral wall acts as an obstacle in the kinetic motion of a kink. It can be a long-range obstacle as modes may enter the continuum even at a considerable distance before the kink meets the other field or impurity. The wall is a selective obstacle experienced only if the pertinent mode is sufficiently excited. In the fermionic case, we have shown that, while passing through a spectral wall, an incoming kink-fermion bound state can be separated into purely bosonic kink, which continues to move to spatial infinity and a fermionic cloud that spreads in the region before the wall.