Mixing with descendant fields in perturbed minimal CFT models

TL;DR

The paper extends the Zamolodchikov analysis of the RG flow between successive minimal models ${\cal M}_p \to {\cal M}_{p-1}$ perturbed by ${\\varphi_{1,3}}$ to include descendant mixing ${\\varphi_{n,n\\pm 3}}$, forming a closed $10$-field set. It develops the necessary three-point function machinery, computes a $10\\times10$ anomalous-dimension matrix, and determines the UV-to-IR mixing coefficients that map UV fields to linear combinations of IR fields and their descendants at the fixed point $g_*$, showing consistency with perturbation theory. The authors also apply Gaiotto's RG domain wall construction to obtain the same UV-IR map coefficients, finding complete agreement in the large-$p$ limit and highlighting the domain-wall method's advantage in handling degeneracies. Together, the work provides a coherent UV-IR map for descendant mixing in perturbed minimal models and cross-validates two complementary approaches to RG flows in 2D CFTs.

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.