Renormalisation group flows of boundary theories

TL;DR

The paper investigates RG flows in two-dimensional boundary conformal field theories, focusing on unitary minimal models. It combines perturbative boundary RG analysis, the g-function as an organizing principle, and numerical Truncated Conformal Space Approach (TCSA) to map boundary flows, showing that perturbations by $\phi_{(1,3)}$ drive boundary conditions to specific superpositions of Cardy states, with $g$ decreasing along flows. In the $c=1$ limit these flows simplify to identities, providing a unifying interpretation that is corroborated by TCSA spectra and by integrable-case analyses via TBA/NLIE. The work thus advances a coherent framework for classifying and testing boundary RG flows, linking conformal boundary-condition classifications with perturbative and numerical tools, and highlighting open questions for joint bulk-boundary dynamics and a potential Landau-Ginzburg-type picture.

Abstract

We review recent developments in the theory of renormalisation group flows in minimal models with boundaries. Among these, we discuss in particular the perturbative calculations of Recknagel et al, not only as a tool to predict the IR endpoints of certain flows, but also as a motivation for considering the particular limiting case of c = 1. By treating this limit, we are able to investigate a wide class of perturbations by considering them as deformations away from the c = 1 point. We also present the truncated conformal space approach as a tool for investigating the space of RG flows and checking particular predictions.