Integrable Quantum Field Theories in Finite Volume: Excited State Energies

TL;DR

This paper introduces a method to compute excited state energies in finite-volume integrable quantum field theories, extending transfer-matrix techniques and thermodynamic Bethe Ansatz to non-conformal models, with explicit results for the Scaling Lee-Yang Model.

Contribution

It generalizes transfer-matrix methods and TBA equations to excited states in non-conformal IQFTs, providing a new computational framework.

Findings

Derived closed integral equations for excited states

Applied method to the Scaling Lee-Yang Model

Validated results with explicit calculations

Abstract

We develop a method of computing the excited state energies in Integrable Quantum Field Theories (IQFT) in finite geometry, with spatial coordinate compactified on a circle of circumference R. The IQFT ``commuting transfer-matrices'' introduced by us (BLZ) for Conformal Field Theories (CFT) are generalized to non-conformal IQFT obtained by perturbing CFT with the operator $\Phi_{1,3}$. We study the models in which the fusion relations for these ``transfer-matrices'' truncate and provide closed integral equations which generalize the equations of Thermodynamic Bethe Ansatz to excited states. The explicit calculations are done for the first excited state in the ``Scaling Lee-Yang Model''.