Open topological defects and boundary RG flows
Anatoly Konechny
TL;DR
The paper develops a framework for open topological defects attached to conformal boundaries in rational CFTs and derives constraints on boundary RG flows triggered by relevant perturbations. It shows that commuting defects force infrared endpoints to admit topological junctions with the same defect and that the open-defect fusion ring is preserved across the flow, while anti-commuting defects relate the two infrared endpoints and demand equal g-factors, forming a Z2-graded structure. The author verifies these principles in diagonal Virasoro minimal models, providing detailed analyses for flows driven by psi13 in the tetracritical and pentacritical Ising models and for direct sums of boundary conditions. The results yield concrete restrictions on possible IR fixed points and hint at deeper connections between defects, integrability, and boundary RG dynamics in RCFTs.
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.