Open topological defects and boundary RG flows

TL;DR

This paper explores how open topological defects influence boundary renormalization group flows in 2D rational conformal field theories, revealing constraints on the endpoints and structure of the flows.

Contribution

It introduces the concept of open topological defects and analyzes their impact on boundary RG flows, providing new constraints and examples in minimal models.

Findings

Open defects that commute or anti-commute with boundary operators impose constraints on RG flow endpoints.

Infrared open defects form a subring under fusion, isomorphic to the initial boundary condition.

Explicit examples in Virasoro minimal models illustrate these theoretical constraints.

Abstract

In the context of two-dimensional rational conformal field theories we consider topological junctions of topological defect lines with boundary conditions. We refer to such junctions as open topological defects. For a relevant boundary operator on a conformal boundary condition we consider a commutation relation with an open defect obtained by passing the junction point through the boundary operator. We show that when there is an open defect that commutes or anti-commutes with the boundary operator there are interesting implications for the boundary RG flows triggered by this operator. The end points of the flow must satisfy certain constraints which, in essence, require the end points to admit junctions with the same open defects. Furthermore, the open defects in the infrared must generate a subring under fusion that is isomorphic to the analogous subring of the original boundary condition. We illustrate these constraints by a number of explicit examples in Virasoro minimal models.