Mixing with descendant fields in perturbed minimal CFT models

TL;DR

This paper investigates the renormalization group flow in minimal conformal field theories, focusing on descendant field mixing, and confirms results through perturbation theory and RG domain wall methods.

Contribution

It extends previous RG analysis to include descendant fields in minimal CFT models and compares different computational approaches for mixing coefficients.

Findings

Identification of specific linear combinations of UV fields flowing to IR fields.

Agreement between perturbation theory and RG domain wall calculations.

Enhanced understanding of field mixing in minimal CFT models.

Abstract

We extend the analysis of the RG trajectory connecting successive minimal CFT models ${\cal M}_p$ and ${\cal M}_{p-1}$ for $p\gg 1$, performed by A. Zamolodchikov, to the fields $\varphi_{n,n\pm 3}$. This required a close investigation of mixing with the descendant fields at the level 2. In particular we identify those specific linear combinations of UV fields which flow to the IR fields $\varphi_{n+3,n}$ and $\varphi_{n-3,n}$. We report also the results of the calculation of the same mixing coefficients through the recent RG domain wall approach by Gaiotto. These results are in complete agreement with the leading order perturbation theory.