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

The vacuum expectation values of the so-called Q-operators of certain integ rable quantum field theories have recently been identified with spectral de terminants of particular Schrodinger operators. In this paper we extend the correspondence to the T-operators, finding that their vacuum expectation v alues also have an interpretation as spectral determinants, As byproducts w e give a simple proof of an earlier conjecture of ours, proved by another r oute 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 integrab le quantum field theory are related to the study of Regge Doles in non-rela tivistic potential scattering. (C) 1999 Elsevier Science B.V. All rights re served.