On relevant boundary perturbations of unitary minimal models

TL;DR

This paper studies how certain boundary deformations in unitary minimal models lead to stable fixed points, resulting in new boundary conditions expressed as superpositions of Cardy states, with implications for boundary RG flows.

Contribution

It provides a perturbative analysis of relevant boundary deformations in minimal models and characterizes the resulting stable boundary fixed points as superpositions of Cardy boundary conditions.

Findings

Boundary deformations flow to stable fixed points

Stable fixed points have no further relevant perturbations

New boundary conditions are superpositions of Cardy states

Abstract

We consider unitary Virasoro minimal models on the disk with Cardy boundary conditions and discuss deformations by certain relevant boundary operators, analogous to tachyon condensation in string theory. Concentrating on the least relevant boundary field, we can perform a perturbative analysis of renormalization group fixed points. We find that the systems always flow towards stable fixed points which admit no further (non-trivial) relevant perturbations. The new conformal boundary conditions are in general given by superpositions of 'pure' Cardy boundary conditions.