Exact conserved quantities on the cylinder II: off-critical case

TL;DR

This paper derives a nonlinear integral equation for a massive quantum system on a cylinder, enabling the calculation of conserved quantities and analyzing their behaviors, advancing understanding of off-critical integrable models.

Contribution

It introduces a novel nonlinear integral equation for off-critical integrable models on the cylinder, linking lattice field theory with quantum conserved quantities.

Findings

Eigenvalues of energy and transfer matrix expressed via solutions of the integral equation

Analytic and asymptotic behaviors of the transfer matrix characterized

Provides tools for studying off-critical integrable quantum systems

Abstract

With the aim of exploring a massive model corresponding to the perturbation of the conformal model [hep-th/0211094] the nonlinear integral equation for a quantum system consisting of left and right KdV equations coupled on the cylinder is derived from an integrable lattice field theory. The eigenvalues of the energy and of the transfer matrix (and of all the other local integrals of motion) are expressed in terms of the corresponding solutions of the nonlinear integral equation. The analytic and asymptotic behaviours of the transfer matrix are studied and given.