Zamalodchikov's C-Theorem and The Logarithmic Conformal Field Theory

TL;DR

This paper investigates the effects of perturbing a conformal field theory with logarithmic operators, revealing conditions under which the c-theorem remains valid despite complex renormalization group behaviors.

Contribution

It extends the understanding of the c-theorem to logarithmic conformal field theories by analyzing beta functions and identifying conditions preserving the theorem.

Findings

Beta function calculated up to two loops for logarithmic operators

Renormalization group trajectories may not always decrease the central charge

Existence of a domain where the c-theorem still applies

Abstract

We consider perturbation of a conformal field theory by a pair of relevant logarithmic operators and calculate the beta function up to two loops. We observe that the beta function can not be derived from a potential. Thus the renormalization group trajectories are not always along decreasing values of the central charge. However there exists a domain of structure constants in which the c-theorem still holds.