Organizing boundary RG flows

TL;DR

This paper introduces a unified rule for boundary RG flows in 2D conformal field theories, extending previous principles to coset models and providing a practical tool for analyzing brane charges and boundary conditions.

Contribution

It generalizes the 'absorption of the boundary spin' principle to all coset models with arbitrary modular invariants, offering a comprehensive framework for boundary RG flows.

Findings

The rule applies to unitary minimal models and parafermion theories.

It enables computation of brane charge groups in N=2 minimal models.

Evidence supports the validity of the proposed boundary RG flow rule.

Abstract

We show how a large class of boundary RG flows in two-dimensional conformal field theories can be summarized in a single rule. This rule is a generalization of the 'absorption of the boundary spin'-principle of Affleck and Ludwig and applies to all theories which have a description as a coset model. We give a formulation for coset models with arbitrary modular invariant partition function and present evidence for the conjectured rule. The second half of the article contains an illustrated section of examples where the rule is applied to unitary minimal models of the A- and D-series, in particular the 3-state Potts model, and to parafermion theories. We demonstrate how the rule can be used to compute brane charge groups in the example of N=2 minimal models.