Log-periodic behavior of finite size effects in field theories with RG limit cycles

TL;DR

This paper investigates the finite size effects in certain field theories with RG limit cycles, revealing periodic behavior in the effective central charge consistent with RG predictions, and distinguishes between massive and massless cases.

Contribution

It provides the first detailed computation of finite size effects in theories with RG limit cycles, highlighting the periodicity of the effective central charge.

Findings

Effective central charge exhibits periodicity consistent with RG limit cycles.

Massless theories show non-singular, periodic behavior across all length scales.

Massive theories have a singularity in the ultra-violet limit.

Abstract

We compute the finite size effects in the ground state energy, equivalently the effective central charge c_{eff}, based on S-matrix theories recently conjectured to describe a cyclic regime of the Kosterlitz-Thouless renormalization group flows. The effective central charge has periodic properties consistent with renormalization group predictions. Whereas c_{eff} for the massive case has a singularity in the very deep ultra-violet, we argue that the massless version is non-singular and periodic on all length scales.