Lee-Yang Model in Presence of Defects

TL;DR

This paper comprehensively analyzes the Lee-Yang model with defects using form factors, bootstrap, and lattice approaches, deriving TBA equations and exploring defect and boundary conditions relevant to integrable quantum field theories.

Contribution

It introduces a combined approach using form factors, bootstrap, and lattice methods to analyze the Lee-Yang model with defects, including deriving TBA equations and studying defect effects.

Findings

Derived ground state TBA equations for the Lee-Yang model with defects.

Analyzed the analytic structure of excited state solutions of TBA.

Calculated Lüscher correction terms for the TBA energy in the large volume limit.

Abstract

I choose the Lee-Yang model and go through different approaches to analyze it using the form factor approach and the bootstrap program, the lattice description and the lattice TBA equations for a full understanding of the model. The bootstrap program aims to explicitly solve 1+1 dimensional integrable quantum field theories. In the first step, called the S-matrix bootstrap, the scattering matrix, is determined from its properties. In developing a defect form factor program the first step is the T-matrix bootstrap. Interacting integrable defect theories are purely transmitting and topological. We analyze both operators localized in the bulk and also on the defect. By finding their solutions, the spectral representation of any correlator can be determined. Next we consider the model on the lattice. The lattice approach allows to obtain both massive and massless excited TBA equations by studying the continuum scaling limit of the associated integrable lattice models. The most important input from the lattice approach is an insight into the analytic structure of the excited state solutions of the TBA equations. Previously this structure had to be guessed. In this thesis we turn our attention to the simplest example of a non-unitary minimal theory, namely, the Lee-Yang minimal model M(2,5). We study the Lee-Yang model on the lattice. We analyze the periodic, boundary and the seam cases in both massive and massless regimes. We derive their ground state TBA equations and analyze the flows between different boundary and defect conditions. Finally, in the large volume limit, we calculate the L\"uscher correction terms of the TBA energy of a one-particle state. We display those ideas in the end of the thesis as this is an important direction of work in string theory, particularly in the AdS/CFT correspondence.