On the relation between Stokes multipliers and the T-Q systems of conformal field theory

TL;DR

This paper explores the connection between Stokes multipliers, T-Q systems, and spectral determinants in integrable quantum field theories, extending known correspondences and providing new insights into PT symmetry and scattering problems.

Contribution

It extends the spectral determinant interpretation from Q-operators to T-operators in integrable quantum field theories, and generalizes a PT symmetry problem.

Findings

Vacuum expectation values of T-operators are spectral determinants.

Provided a simple proof of a previous conjecture.

Connected integrable Q-operators with Regge poles in scattering.

Abstract

The vacuum expectation values of the so-called Q-operators of certain integrable quantum field theories have recently been identified with spectral determinants of particular Schrodinger operators. In this paper we extend the correspondence to the T-operators, finding that their vacuum expectation values also have an interpretation as spectral determinants. As byproducts we give a simple proof of an earlier conjecture of ours, proved by another route by Suzuki, and generalise a problem in PT symmetric quantum mechanics studied by Bender and Boettcher. We also stress that the mapping between Q-operators and Schrodinger equations means that certain problems in integrable quantum field theory are related to the study of Regge poles in non-relativistic potential scattering.