Domain Walls for Two-Dimensional Renormalization Group Flows

TL;DR

This paper constructs explicit algebraic models of domain walls acting as interfaces between UV and IR conformal field theories in two dimensions, matching known operator mixing results and applicable to various RG flows.

Contribution

It provides a novel algebraic construction of RG domain walls between minimal models, enabling detailed analysis of operator mappings in 2D conformal field theories.

Findings

Reproduces leading order operator mixing in agreement with conformal perturbation theory

Provides an explicit algebraic framework for RG domain walls in 2D CFTs

Applicable to multiple known RG flows in two dimensions

Abstract

Renormalization Group domain walls are natural conformal interfaces between two CFTs related by an RG flow. The RG domain wall gives an exact relation between the operators in the UV and IR CFTs. We propose an explicit algebraic construction of the RG domain wall between consecutive Virasoro minimal models in two dimensions. Our proposal passes a stringent test: it reproduces in detail the leading order mixing of UV operators computed in the conformal perturbation theory literature. The algebraic construction can be applied to a variety of known RG flows in two dimensions.