Excited state Destri-De Vega equation for sine-Gordon and restricted sine-Gordon models

We derive a generalization of the Destri-De Vega equation governing the scaling functions of some excited states in the sine-Gordon theory. In particular, configurations with an even number of holes and no strings are analyzed and their UV limits found to match some of the conformal dimensions of the corresponding compactified massless free boson. Quantum group reduction allows to interpret some of our results as scaling functions of excited states of Restricted sine-Gordon theory, i.e. minimal models perturbed by φ13 in their massive regime. In particular we are able to reconstruct the scaling functions of the off-critical deformations of all the scalar primary states on the diagonal of the Kac table.