Open topological defects and boundary RG flows

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.

arXiv comment26 pages; v.2: section 3 rewritten and now includes a detailed discussion of RG counterterms, new example added at the end of section 4.2, extended discussion of the ψ_1,2 boundary flow in the Pentacritical model, minor improvements throughout the text

References in corpus (16)

• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• TFT construction of RCFT correlators I: Partition functions
• Duality and defects in rational conformal field theory
• Generalised twisted partition functions
• Kramers-Wannier duality from conformal defects
• On the Boundary Entropy of One-dimensional Quantum Systems at Low Temperature
• Boundary structure constants for the A-series Virasoro minimal models
• TBA and TCSA with boundaries and excited states
• Defect Lines and Boundary Flows
• Edge Critical Behaviour of the 2-Dimensional Tri-critical Ising Model
• Boundary flows in minimal models
• On relevant boundary perturbations of unitary minimal models
• Perturbed Defects and T-Systems in Conformal Field Theory
• On Perturbations of Unitary Minimal Models by Boundary Condition Changing Operators
• Non-local conserved charges from defects in perturbed conformal field theory
• Infrared properties of boundaries in 1-d quantum systems

Cited by in corpus (9)

• Remarks on Boundaries, Anomalies, and Noninvertible Symmetries
• Open spin chain realization of topological defect on 1d Ising model and boundary and bulk symmetry
• Noninvertible Symmetry-Resolved Affleck-Ludwig-Cardy Formula and Entanglement Entropy from the Boundary Tube Algebra
• Generalized Symmetry Resolution of Entanglement in CFT for Twisted and Anyonic sectors
• Scaling of the Formation Probabilities and Universal Boundary Entropies in the Quantum XY Spin Chain
• Universal time evolution of string order parameter in quantum critical systems with boundary invertible or non-invertible symmetry breaking
• Conformal Defects from String Field Theory
• Revisiting the symmetry-resolved entanglement for non-invertible symmetries in $1+1$d conformal field theories
• Lattice models from CFT on surfaces with holes I: Torus partition function via two lattice cells