Two-dimensional massive integrable models on a torus

TL;DR

This paper develops a novel approach to describe the finite-volume thermodynamics of massive integrable quantum field theories on a torus using a loop path integral and Hubbard-Stratonovich transformation, connecting it to the Thermodynamical Bethe Ansatz.

Contribution

It introduces a new loop-based path integral formulation and explicit evaluation method for the finite-volume thermodynamics of integrable models on a torus, linking it to mean field theory and the TBA.

Findings

Explicit expression for the torus partition function in terms of oscillator expectation values.

Connection between the mean field limit and the thermodynamic Bethe ansatz.

A novel loop and Hubbard-Stratonovich based approach to finite-volume integrable QFTs.

Abstract

The finite-volume thermodynamics of a massive integrable QFT is described in terms of a grand canonical ensemble of loops immersed in a torus and interacting through scattering factors associated with their intersections. The path integral of the loops is evaluated explicitly after decoupling the pairwise interactions by a Hubbard-Stratonovich transformation. The HS fields are holomorphic fields depending on the rapidity and can be expanded in elementary oscillators. The torus partition function is expressed as certain expectation value in the Fock space of these oscillators. In the limit where one of the periods of the torus becomes asymptotically large, the effective field theory becomes mean field type. The mean field describes the infinite-volume thermodynamics which is solved by the Thermodynamical Bethe Ansatz.