Renormalization group limit cycles and field theories for elliptic S-matrices -: art. no. P08004

The renormalization group (RG) for maximally anisotropic su(2) current interactions in two dimensions is shown to be cyclic at one-loop level. The fermionized version of the model exhibits spin-charge separation of the four-fermion interactions and has Z(4) symmetry. It is proposed that the S-matrices for these theories are the elliptic Zamolodchikov and Mussardo-Penati S-matrices. The S-matrix parameters are related to Lagrangian parameters by matching the period of the RG. All models exhibit two characteristic signatures of an RG limit cycle: periodicity of the S-matrix as a function of energy and the existence of an infinite number of resonance poles satisfying Russian doll scaling.