TBA equations for excited states in the sine-Gordon model

We propose thermodynamic Bethe ansatz (TBA) integral equations for multiparticle soliton (fermion) states in the sine-Gordon (massive Thirring) model. This is based on T-system and Y-system equations, which follow from the Bethe ansatz solution in the light-cone lattice formulation of the model. Even and odd charge sectors are treated on an equal footing, corresponding to periodic and twisted boundary conditions, respectively. The analytic properties of the Y-system functions are conjectured on the basis of the large volume solution of the system, which we find explicitly. A simple relation between the TBA Y-functions and the counting function variable of the alternative non-linear integral equation (Destri-deVega equation) description of the model is given. At the special value beta(2) = 6pi of the sine-Gordon coupling, exact expressions for energy and momentum eigenvalues of one-particle states are found.