Excited states in some simple perturbed conformal field theories

TL;DR

This paper develops a method using analytic continuation to derive exact integral equations for finite-volume energy levels in certain perturbed conformal field theories, with detailed analysis of the N=2 case.

Contribution

It introduces a novel approach for calculating excited states in non-unitary minimal models via analytic continuation, providing general results applicable to other models.

Findings

Derived exact integral equations for energy levels in perturbed minimal models

Detailed analysis of the N=2 case

General results relevant to excited states in various models

Abstract

The method of analytic continuation is used to find exact integral equations for a selection of finite-volume energy levels for the non-unitary minimal models $M_{2,2N+3}$ perturbed by their $\varphi_{13}$ operators. The N=2 case is studied in particular detail. Along the way, we find a number of general results which should be relevant to the study of excited states in other models.