Nonlinear integral equations for complex affine Toda models associated with simply laced Lie algebras

Abstract

A set of coupled nonlinear integral equations (NLIE) is derived for a class of models connected to the quantum group Uq(θ) (θ simply laced Lie algebra), which are solvable using the Bethe ansatz; these equations describe arbitrary excited states of a system with finite spatial length L They generalize the simpler NLIE of the sine-Gordon/massive Thirring model to affine Toda field theory with imaginary coupling constant. As an application, the central charge and all the conformal weights of the UV conformal field theory are extracted in a straightforward manner. The quantum group truncation for q at a root of unity is discussed in detail; in the UV limit we recover through this procedure the ..