Plateaux Transitions from S-matrices based on SL(2,Z) Invariant Field Theories

TL;DR

This paper introduces a scattering description for boundary perturbations in a c=1 SL(2,Z) invariant conformal field theory, revealing a staircase pattern in boundary free energy via thermodynamic Bethe ansatz analysis.

Contribution

It develops a boundary scattering framework for SL(2,Z) invariant theories and demonstrates the occurrence of quantized plateaux in boundary free energy.

Findings

Boundary free energy exhibits integer-valued plateaux.

Bulk S-matrices resemble Zamolodchikov's staircase model.

Thermodynamic Bethe ansatz confirms the staircase behavior.

Abstract

A scattering scattering description is proposed for a boundary perturbation of a c=1 SL(2,Z) invariant conformal field theory. The bulk massless S-matrices are of the form of Zamolodchikov's staircase model. Using the boundary version of the thermodynamic Bethe ansatz, we show that the boundary free energy goes through a series of integer valued plateaux as a function of system size.