Two Dimensional Renormalization Group Flows in Next to Leading Order

TL;DR

This paper enhances the analysis of two-dimensional RG flows between minimal conformal field theories by including second-order corrections, improving the accuracy of IR limit predictions and relating results to recent domain wall proposals.

Contribution

It introduces second-order coupling corrections to RG flow analysis, refining IR limit identification and connecting to recent theoretical proposals.

Findings

Computed beta functions and anomalous dimensions with next-to-leading order accuracy.

Improved matching of IR fields with linear combinations of IR theory fields.

Discussed the relation of results with Gaotto's RG domain wall proposal.

Abstract

Zamolodchikov's famous analysis of the RG trajectory connecting successive minimal CFT models $M_p$ and $M_{p-1}$ for $p\gg 1$, is improved by including second order in coupling constant corrections. This allows to compute IR quantities with next to leading order accuracy of the $1/p$ expansion. We compute in particular, the beta function and the anomalous dimensions for certain classes of fields. As a result we are able to identify with a greater accuracy the IR limit of these fields with certain linear combination of the IR theory $M_{p-1}$. We discuss the relation of these results with Gaotto's recent RG domain wall proposal.