g-function flow in perturbed boundary conformal field theories

TL;DR

This paper investigates the behavior of the g-function in perturbed boundary conformal field theories, specifically the Yang-Lee model, using various theoretical approaches to understand boundary flows and their relation to bulk perturbations.

Contribution

It provides a detailed analysis of the g-function in perturbed boundary conformal field theories, clarifying the applicability of TBA equations and deriving exact relations between UV and IR parameters.

Findings

TBA equations describe massless boundary flows up to a constant

TBA equations correctly give the linear term in the massive case

The ratio of g-functions for different boundary conditions is accurately predicted

Abstract

The g-function was introduced by Affleck and Ludwig as a measure of the ground state degeneracy of a conformal boundary condition. We consider this function for perturbations of the conformal Yang-Lee model by bulk and boundary fields using conformal perturbation theory, the truncated conformal space approach and the thermodynamic Bethe Ansatz (TBA). We find that the TBA equations derived by LeClair et al describe the massless boundary flows, up to an overall constant, but are incorrect when one considers a simultaneous bulk perturbation; however the TBA equations do correctly give the `non-universal' linear term in the massive case, and the ratio of g-functions for different boundary conditions is also correctly produced. This ratio is related to the Y-system of the Yang-Lee model and by comparing the perturbative expansions of the Y-system and of the g-functions we obtain the exact relation between the UV and IR parameters of the massless perturbed boundary model.