g-function flow in perturbed boundary conformal field theories

The g-function was introduced by Affleck and Ludwig as a measure of the gro und state degeneracy of a conformal boundary condition. We consider this fu nction for perturbations of the conformal Yang-Lee model by bulk and bounda ry fields using conformal perturbation theory (CPT), the truncated conforma l space approach (TCSA) and the thermodynamic Bethe Ansatz (TBA). We find t hat the TEA equations derived by LeClair et al. describe the massless bound ary flows, up to an overall constant, but are incorrect when one considers a simultaneous bulk perturbation; however the TEA equations do correctly gi ve the 'non-universal' linear term in the massive case, and the ratio of g- functions for different boundary conditions is also correctly produced. Thi s ratio is related to the Y-system of the Yang-Lee model and by comparing t he 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 pertur bed boundary model. (C) 2000 Elsevier Science B.V. All rights reserved.