Renormalization group limit-cycles and field theories for elliptic S-matrices

TL;DR

This paper demonstrates that certain 2D anisotropic su(2) current interaction models exhibit cyclic renormalization group behavior, with their S-matrices described by elliptic functions, revealing unique resonance and scaling properties.

Contribution

It establishes a connection between cyclic RG flows and elliptic S-matrices, providing a new perspective on integrable models with limit cycles in quantum field theory.

Findings

RG flow is cyclic at one loop for the model.

S-matrices are elliptic functions related to RG parameters.

Models show infinite resonance poles with Russian doll scaling.

Abstract

The renormalization group for maximally anisotropic su(2) current interactions in 2d is shown to be cyclic at one loop. The fermionized version of the model exhibits spin-charge separation of the 4-fermion interactions and has Z_4 symmetry. It is proposed that the S-matrices for these theories are the elliptic S-matrices of Zamolodchikov and Mussardo-Penati. The S-matrix parameters are related to lagrangian parameters by matching the period of the renormalization group. 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.