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

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. (C) 2004 Elsevier B.V. All rights reserved.