A Defect Verlinde Formula

Abstract

We revisit the problem of boundary excitations at a topological boundary or junction defects between topological boundaries in non-chiral bosonic topological orders in 2+1 dimensions. Based on physical considerations, we derive a formula that relates the fusion rules of the boundary excitations, and the "half-linking" number between condensed anyons and confined boundary excitations. This formula is a direct analogue of the Verlinde formula. We also demonstrate how these half-linking numbers can be computed in explicit Abelian and non-Abelian examples. As a fundamental property of topological orders and their allowed boundaries, this should also find applications in finding suitable platforms realizing quantum computing devices.

arXiv comment9 pages, 2 figures

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Cited by in corpus (12)

• Asymptotic density of states in 2d CFTs with non-invertible symmetries
• Topological holography, quantum criticality, and boundary states
• Entanglement bootstrap approach for gapped domain walls
• A (Dummy's) Guide to Working with Gapped Boundaries via (Fermion) Condensation
• Computing data for Levin-Wen with defects
• Towards Non-Invertible Anomalies from Generalized Ising Models
• Ishibashi States, Topological Orders with Boundaries and Topological Entanglement Entropy II -- Cutting through the boundary
• U(1) spin Chern-Simons theory and Arf invariants in two dimensions
• Galois Orbits of TQFTs: Symmetries and Unitarity
• Symmetry Fractionalized (Irrationalized) Fusion Rules and Two Domain-Wall Verlinde Formulae
• Duality via Sequential Quantum Circuit in the Topological Holography Formalism
• Remote detectability from entanglement bootstrap I: Kirby's torus trick