CFT Correlators for Cardy Bulk Fields via String-Net Models

Abstract

We show that string-net models provide a novel geometric method to construct invariants of mapping class group actions. Concretely, we consider string-net models for a modular tensor category $\mathcal{C}$. We show that the datum of a specific commutative symmetric Frobenius algebra in the Drinfeld center $Z(\mathcal{C})$ gives rise to invariant string-nets. The Frobenius algebra has the interpretation of the algebra of bulk fields of the conformal field theory in the Cardy case.

References in corpus (14)

• String-net condensation: A physical mechanism for topological phases
• TFT construction of RCFT correlators III: Simple currents
• Correspondences of ribbon categories
• TFT construction of RCFT correlators IV: Structure constants and correlation functions
• Quantum computation with Turaev-Viro codes
• TFT construction of RCFT correlators II: Unoriented world sheets
• Cardy algebras and sewing constraints, I
• Turaev-Viro invariants as an extended TQFT
• String-net model of Turaev-Viro invariants
• Higher Frobenius-Schur Indicators for Pivotal Categories
• Morita classes of algebras in modular tensor categories
• On two approaches to 3-dimensional TQFTs
• Consistent systems of correlators in non-semisimple conformal field theory
• The logarithmic Cardy case: Boundary states and annuli

Cited by in corpus (1)

• Bulk from boundary in finite CFT by means of pivotal module categories