The k-folded sine-Gordon model in finite volume

TL;DR

This paper studies the k-folded sine-Gordon model in finite volume, analyzing its energy spectrum and vacuum expectations using multiple methods, and confirms the consistency of these approaches, supporting the NLIE method and instanton contributions.

Contribution

It introduces a comprehensive analysis of the k-folded sine-Gordon model combining multiple methods, validating the NLIE approach and providing evidence for conjectured vacuum expectation formulas.

Findings

Methods are consistent in predicting ground state energy and spectrum.

Supports the NLIE method with a twist parameter.

Provides evidence for the exact vacuum expectation value formula.

Abstract

We consider the k-folded sine-Gordon model, obtained from the usual version by identifying the scalar field after k periods of the cosine potential. We examine (1) the ground state energy split, (2) the lowest lying multi-particle state spectrum and (3) vacuum expectation values of local fields in finite spatial volume, combining the Truncated Conformal Space Approach, the method of the Destri-de Vega nonlinear integral equation (NLIE) and semiclassical instanton calculations. We show that the predictions of all these different methods are consistent with each other and in particular provide further support for the NLIE method in the presence of a twist parameter. It turns out that the model provides an optimal laboratory for examining instanton contributions beyond the dilute instanton gas approximation. We also provide evidence for the exact formula for the vacuum expectation values conjectured by Lukyanov and Zamolodchikov.