Rg Flows in the $D$-Series of Minimal Cfts

TL;DR

This paper investigates the renormalization group flows in minimal conformal field theories of the D-series, showing how perturbations induce flows to lower models and highlighting an exceptional case involving the 3-state Potts CFT.

Contribution

It provides a detailed analysis of RG flows in D-series minimal CFTs using thermodynamic Bethe Ansatz and conformal perturbation theory, including an exceptional flow case.

Findings

RG flows in D-series minimal CFTs lead to lower models

The 3-state Potts CFT flows to tricritical Ising CFT under perturbation

Flow directions in A-series are opposite for the exceptional case

Abstract

Using results of the thermodynamic Bethe Ansatz approach and conformal perturbation theory we argue that the $\phi_{1,3}$-perturbation of a unitary minimal $(1+1)$-dimensional conformal field theory (CFT) in the $D$-series of modular invariant partition functions induces a renormalization group (RG) flow to the next-lower model in the $D$-series. An exception is the first model in the series, the 3-state Potts CFT, which under the $\ZZ_2$-even $\phi_{1,3}$-perturbation flows to the tricritical Ising CFT, the second model in the $A$-series. We present arguments that in the $A$-series flow corresponding to this exceptional case, interpolating between the tetracritical and the tricritical Ising CFT, the IR fixed point is approached from ``exactly the opposite direction''. Our results indicate how (most of) the relevant conformal fields evolve from the UV to the IR CFT.