Scaling Functions in the Odd Charge Sector of Sine-Gordon/Massive Thirring Theory

TL;DR

This paper extends a known non-linear integral equation to include odd topological charge states in sine-Gordon/massive Thirring theory, enabling complete analysis of finite size energy levels and matching with existing data.

Contribution

The authors conjecture an extension of the NLIE to odd topological charges, completing the spectral description of the sine-Gordon/massive Thirring models.

Findings

Extended NLIE matches Truncated Conformal Space data

Complete control over finite size energy levels

Compatibility with known local Hilbert space facts

Abstract

A non-linear integral equation (NLIE) governing the finite size effects of excited states of even topological charge in the sine-Gordon (sG) / massive Thirring (mTh) field theory, deducible from a light-cone lattice formulation of the model, has been known for some time. In this letter we conjecture an extension of this NLIE to states with odd topological charge, thus completing the spectrum of the theory. The scaling functions obtained as solutions to our conjectured NLIE are compared successfully with Truncated Conformal Space data and the construction is shown to be compatible with all other facts known about the local Hilbert spaces of sG and mTh models. With the present results we have achieved a full control over the finite size behaviour of energy levels of sG/mTh theory.