Finite size effects in quantum field theories with boundary from scattering data

TL;DR

This paper establishes a new relation between finite size corrections and scattering data in 1+1 dimensional quantum field theories with boundaries, supported by analytical and numerical evidence.

Contribution

It generalizes a boundary scattering relation from the Lee-Yang model to all 1+1 dimensional boundary quantum field theories, using multiple analytical methods.

Findings

Derived a boundary finite size correction relation from scattering data.

Validated the relation analytically and numerically across models.

Extended previous boundary scattering results to general 1+1D theories.

Abstract

We derive a relation between leading finite size corrections for a 1+1 dimensional quantum field theory on a strip and scattering data, which is very similar in spirit to the approach pioneered by Luscher for periodic boundary conditions. The consistency of the results is tested both analytically and numerically using thermodynamic Bethe Ansatz, Destri-de Vega nonlinear integral equation and classical field theory techniques. We present strong evidence that the relation between the boundary state and the reflection factor one-particle couplings, noticed earlier by Dorey et al. in the case of the Lee-Yang model extends to any boundary quantum field theory in 1+1 dimensions.