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arXiv · hep-th/0301042

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

A. Leclair·J. M. Roman·G. Sierra
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Abstract

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. Using bosonization, we show that the theory has $U_q (\hat{sl(2)})$ quantum affine symmetry, with $q$ {\it real}. Based on this symmetry, we study two possible S-matrices for the theory, differing only by overall scalar factors. We argue that one S-matrix corresponds to a continuum limit of the XXZ spin chain in the anti-ferromagnetic domain $Δ< -1$. The latter S-matrix has a periodicity in energy consistent with the cyclicity of the RG. We conjecture that this S-matrix describes the cyclic regime of the Kosterlitz-Thouless flows. The other S-matrix we investigate is an analytic continuation of the usual sine-Gordon one. It has an infinite number of resonances with masses that have a Russian doll scaling behavior that is also consistent with the period of the RG cycles computed from the beta-function. Closure of the bootstrap for this S-matrix leads to an infinite number of particles of higher spin with a mass formula suggestive of a string theory.

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A. Leclair, J. M. Roman, G. Sierra. 2003-06-27. Russian Doll Renormalization Group, Kosterlitz-Thouless Flows, and the Cyclic sine-Gordon model. https://doi.org/10.1016/j.nuclphysb.2003.09.032

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