Boundary entropy of integrable perturbed $SU(2)_k$ WZNW

TL;DR

This paper computes the boundary entropy in an integrable $SU(2)_k$ WZNW model with boundary, addressing divergences in non-diagonal scattering cases and relating UV and IR limits to known g-functions.

Contribution

It applies new analytical methods to calculate boundary entropy in non-diagonal integrable theories, resolving divergence issues and connecting results to established g-functions.

Findings

Boundary entropy is infinite without subtraction in non-diagonal scattering cases.

A subtraction procedure makes the boundary entropy finite.

The UV-IR difference matches known g-functions for even levels.

Abstract

We apply the recently developped analytical methods for computing the boundary entropy, or the g-function, in integrable theories with non-diagonal scattering. We consider the particular case of the current-perturbed $SU(2)_k$ WZNW model with boundary and compute the boundary entropy for a specific boundary condition. The main problem we encounter is that in case of non-diagonal scattering the boundary entropy is infinite. We show that this infinity can be cured by a subtraction. The difference of the boundary entropies in the UV and in the IR limits is finite, and matches the known g-functions for the unperturbed $SU(2)_k$ WZNW model for even values of the level.