g-function flow in perturbed boundary conformal field theories

TL;DR

The paper investigates g-functions in perturbed boundary conformal field theories using CPT, TCSA, and TBA in the Yang-Lee model. It finds that TBA g-functions correctly describe massless boundary flows (up to a constant) but fail for simultaneous bulk perturbations in the massive case, though they accurately capture ratios of g-functions via a simple Y-system relation. The study establishes exact UV–IR relations for massless perturbed boundary models and highlights nuanced contour prescriptions essential for consistent TBA results. Across methods, the work demonstrates both the strengths and limitations of TBA in non-unitary, perturbed boundary CFTs and clarifies how boundary flows connect to the underlying scattering data and Y-system structure.

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.