Russian Doll Renormalization Group, Kosterlitz-Thouless Flows, and the Cyclic sine-Gordon model

We investigate the previously proposed cyclic regime of the Kosterlitz-Thouless renormalization group (RG) flows. The period of one cycle is computed in terms of the RG invariant. Mapping this theory to the sine-Gordon model, we conjecture a particle spectrum and S-matrix. The S-matrix has an infinite number of resonances with masses that have a Russian doll scaling behavior that is consistent with the period of the RG cycles computed from the beta-function. Closure of the bootstrap for the S-matrix leads to an infinite number of particles of higher spin with a mass formula suggestive of a string theory