Boundary States and Anomalous Symmetries of Fermionic Minimal Models

Abstract

The fermionic minimal models are a recently-introduced family of two-dimensional spin conformal field theories. We determine all of their conformal boundary states and potentially anomalous ${\mathbb{Z}}_2$ global symmetries. The latter task hinges upon on a conjecture about $\mathfrak{su}(2)$ affine parities generalising an earlier result known to have an interpretation in terms of Fermat curves. Our results indicate a close connection between several properties of the models, including the matching of the sizes of the SPT classes of boundary states, the existence of anomalous ${\mathbb{Z}}_2$ symmetries, and the vanishing of the Ramond-Ramond sector, for which we provide an explanation.

arXiv comment34 pages, 8 figures

References in corpus (9)

• Fermion Path Integrals And Topological Phases
• Fermionic Symmetry Protected Topological Phases and Cobordisms
• Orbifold groupoids
• Interacting topological phases and modular invariance
• State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
• A Web of 2d Dualities: ${\mathbf{Z}}_2$ Gauge Fields and Arf Invariants
• Fermionic minimal models
• Boundary conformal field theory and symmetry protected topological phases in $2+1$ dimensions
• Discrete symmetries of unitary minimal conformal theories

Cited by in corpus (2)

• Crosscap States in Integrable Field Theories and Spin Chains
• Fermionization of conformal boundary states