RG Flows of Non-Unitary Minimal CFTs

TL;DR

This paper investigates the renormalization group flows of non-unitary minimal conformal field theories perturbed by a specific operator, revealing new IR fixed points and their relation to modular invariants.

Contribution

It identifies a new IR fixed point in non-unitary minimal CFTs under perturbation and connects the flow of modular invariants to these fixed points.

Findings

Discovery of a new IR fixed point corresponding to (2p-q,p) minimal CFT

Identification of the perturbing operator near the IR fixed point as irrelevant ,1

Flow of non-diagonal modular invariants into corresponding fixed points

Abstract

In this paper we study the renormalization group flow of the $(p,q)$ minimal (non-unitary) CFT perturbed by the $\Phi_{1,3}$ operator with a positive coupling. In the perturbative region $q>>(q-p)$, we find a new IR fixed point which corresponds to the $(2p-q,p)$ minimal CFT. The perturbing field near the new IR fixed point is identified with the irrelevent $\Phi_{3,1}$ operator. We extend this result to show that the non-diagonal ($(A,D)$-type) modular invariant partition function of the $(p,q)$ minimal CFT flows into the $(A,D)$-type partition function of the $(2p-q,p)$ minimal CFT and the diagonal partition function into the diagonal.