-function flow in perturbed boundary conformal field theories

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 (CPT), the truncated conformal space approach (TCSA) 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. 1

The scaling supersymmetric Yang–Lee model with boundary

“…Moreover, we consider 12) where the boundary scale θ B is finite. For the sign − in the limit (2.11), the boundary S matrix reduces to S(θ − θ B ) −1 [14], and we obtain…”

“…Indeed, the boundary S matrix (2.3) coincides with that of the first sine-Gordon breather [36] with γ = 16π/3, and with the parameters η , ϑ of [9] taking the values [14] …”

“…Following [35], [14] , we consider the boundary YL model which is defined by the perturbed action (1.2), where the CFT is M(2/5), the CBC corresponds to the cell (1 , 3) of the Kac …”

“…Note that our expression (2.6) for the boundary entropy differs in the third term in the brackets from the one given in Refs. [13] and [14]. This term originates from the exclusion [37], [38] of the Bethe Ansatz root at zero rapidity.…”

Bayesian sample size determination in non‐sequential clinical trials: Statistical aspects and some regulatory considerations

“…Because each model has very different properties, it is difficult to identify the general features. For example, the bulk flow studied in [10,11,16] focused on the non-unitary Lee-Yang model. Features of these flows could be attributed to the lack of unitarity, rather than being generic to bulk flows.…”