Renormalization group flow with unstable particles

TL;DR

This paper studies how the renormalization group flow in a 2D quantum field theory with unstable particles affects the central charge and conformal dimensions, identifying the associated conformal field theories as particles disappear.

Contribution

It provides a detailed analysis of the RG flow in the SU(3)_{2}-homogeneous Sine-Gordon model, revealing the evolution of operator content with unstable particles.

Findings

Identified the conformal field theories corresponding to different RG flow stages.

Mapped the operator content as unstable particles vanish.

Analyzed the behavior of the Virasoro central charge during the flow.

Abstract

The renormalization group flow of an integrable two dimensional quantum field theory which contains unstable particles is investigated. The analysis is carried out for the Virasoro central charge and the conformal dimensions as a function of the renormalization group flow parameter. This allows to identify the corresponding conformal field theories together with their operator content when the unstable particles vanish from the particle spectrum. The specific model considered is the $SU(3)_{2}$-homogeneous Sine-Gordon model.