On Perturbations of Unitary Minimal Models by Boundary Condition Changing Operators

TL;DR

This paper studies boundary perturbations in unitary minimal models, specifically analyzing how boundary condition changing operators influence the renormalization group flows and providing a diagrammatic representation of these flows.

Contribution

It explicitly maps the perturbative RG flows for boundary condition changing operators in unitary minimal models and introduces a simple diagrammatic method to visualize these flows.

Findings

Mapped out the space of RG flows for phi_{1,3} boundary perturbations

Provided insights into more general phi_{r,r+2} boundary perturbations

Developed a diagrammatic representation for boundary flow spaces

Abstract

In this note we consider boundary perturbations in the A-Series unitary minimal models by phi_{r,r+2} fields on superpositions of boundaries. In particular, we consider perturbations by boundary condition changing operators. Within conformal perturbation theory we explicitly map out the space of perturbative renormalisation group flows for the example phi_{1,3} and find that this sheds light on more general phi_{r,r+2} perturbations. Finally, we find a simple diagrammatic representation for the space of flows from a single Cardy boundary condition.