Fusion of conformal interfaces and bulk induced boundary RG flows

TL;DR

This paper investigates how conformal interfaces that change the radius of a free boson theory fuse with boundary conditions, revealing insights into boundary RG flows and singularity structures.

Contribution

It proposes a conjecture linking radius-changing interfaces with boundary RG flow endpoints and analyzes fusion singularities in this context.

Findings

Fusion singularities reveal RG logarithms and their resummation into power singularities.

Fusing radius-changing interfaces with exceptional boundary conditions models boundary RG flows.

Discussion on quantities needed for non-perturbative understanding of fusion processes.

Abstract

We consider the basic radius changing conformal interface for a free compact boson. After investigating different theoretical aspects of this object we focus on the fusion of this interface with conformal boundary conditions. At fractions of the self-dual radius there exist exceptional D-branes. It was argued in [1] that changing the radius in the bulk induces a boundary RG flow. Following [2] we conjecture that fusing the basic radius changing interface (that changes the radius from a fraction of the self-dual radius) with the exceptional boundary conditions gives the boundary condition which is the end point of the RG flow considered in [1]. By studying the fusion singularities we recover RG logarithms and see, in particular instances, how they get resummed into power singularities. We discuss what quantities need to be calculated to gain full non-perturbative control over the fusion.