One-point functions in perturbed boundary conformal field theories

TL;DR

This paper investigates one-point functions in perturbed boundary conformal field theories, using multiple methods to analyze bulk and boundary fields, and discovers new identities and boundary instabilities.

Contribution

It provides a combined analysis of one-point functions in the scaling Lee-Yang model with boundary and bulk perturbations, correcting previous boundary state expressions and deriving new off-critical identities.

Findings

Good agreement between truncated conformal space and form-factor methods

Correction to the boundary state expression by Ghoshal and Zamolodchikov

Discovery of a novel off-critical identity between cylinder partition functions

Abstract

We consider the one-point functions of bulk and boundary fields in the scaling Lee-Yang model for various combinations of bulk and boundary perturbations. The one-point functions of the bulk fields are analysed using the truncated conformal space approach and the form-factor expansion. Good agreement is found between the results of the two methods, though we find that the expression for the general boundary state given by Ghoshal and Zamolodchikov has to be corrected slightly. For the boundary fields we use thermodynamic Bethe ansatz equations to find exact expressions for the strip and semi-infinite cylinder geometries. We also find a novel off-critical identity between the cylinder partition functions of models with differing boundary conditions, and use this to investigate the regions of boundary-induced instability exhibited by the model on a finite strip.