Bulk flows in Virasoro minimal models with boundaries

TL;DR

This paper investigates how boundary conditions in Virasoro minimal models evolve under relevant bulk perturbations, identifying the resulting boundary conditions after the flow using perturbative and non-perturbative methods.

Contribution

It provides a detailed analysis of boundary RG flows induced by bulk perturbations in Virasoro minimal models, combining perturbative and non-perturbative techniques to determine endpoint boundary conditions.

Findings

Boundary conditions flow to conformal boundary states in the (m-1)st model.

Identification of the endpoint boundary condition for arbitrary initial conditions.

Application of combined perturbative and non-perturbative methods to boundary flows.

Abstract

The behaviour of boundary conditions under relevant bulk perturbations is studied for the Virasoro minimal models. In particular, we consider the bulk deformation by the least relevant bulk field which interpolates between the mth and (m-1)st unitary minimal model. In the presence of a boundary this bulk flow induces an RG flow on the boundary, which ensures that the resulting boundary condition is conformal in the (m-1)st model. By combining perturbative RG techniques with insights from defects and results about non-perturbative boundary flows, we determine the endpoint of the flow, i.e. the boundary condition to which an arbitrary boundary condition of the mth theory flows to.