Fermionization of conformal boundary states

Abstract

We construct the complete set of boundary states of two-dimensional fermionic CFTs using that of the bosonic counterpart. We see that there are two groups of boundary conditions, which contributes to the open-string partition function by characters with integer coefficients, or with $\sqrt{2}$ times integer coefficients. We argue that, using the argument of [JHEP 09 (2020) 018], this $\sqrt{2}$ indicates a single unpaired Majorana zero mode, and that these two groups of boundary conditions are mutually incompatible. We end the paper by mentioning a possible interpretation of the result in terms of the entanglement entropy.

arXiv comment11 pages

References in corpus (48)

• Unpaired Majorana fermions in quantum wires
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Topological phases of fermions in one dimension
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Remarks on entanglement entropy for gauge fields
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Topological Defects on the Lattice I: The Ising model
• Spin TQFTs and fermionic phases of matter
• State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
• Unusual Corrections to Scaling in Entanglement Entropy
• A Web of 2d Dualities: ${\mathbf{Z}}_2$ Gauge Fields and Arf Invariants
• On S-Duality in Abelian Gauge Theory
• Symmetry breaking boundaries I. General theory
• Conformal boundary states for free bosons and fermions
• Physics at the entangling surface
• Dual Boundary Conditions in 3d SCFT's
• Symmetry breaking boundaries II. More structures; examples
• Fermionic minimal models
• Branes: from free fields to general backgrounds
• A classifying algebra for boundary conditions
• A worldsheet extension of O(d,d;Z)
• 3d Abelian Gauge Theories at the Boundary
• Orbifold boundary states from Cardy's condition
• Boundary conformal field theory and symmetry protected topological phases in $2+1$ dimensions
• Anomaly of the Electromagnetic Duality of Maxwell Theory
• Topological Superconductors on Superstring Worldsheets
• Fermionic CFTs and classifying algebras
• Defects in the Tri-critical Ising model
• Boundary States of c=1 and 3/2 Rational Conformal Field Theories
• 3d Abelian Dualities with Boundaries
• Two More Fermionic Minimal Models
• Mixed global anomalies and boundary conformal field theories
• GSO projections via SPT phases
• Fermionization and boundary states in 1+1 dimensions
• Open Strings in Simple Current Orbifolds
• Electromagnetic Duality and Entanglement Anomalies
• Comments on Defining Entanglement Entropy
• Lower bound on the entropy of boundaries and junctions in 1+1d quantum critical systems
• What Symmetries are Preserved by a Fermion Boundary State?
• Master 3d Bosonization Duality with Boundaries
• Boundary RG Flows for Fermions and the Mod 2 Anomaly
• Superconformal defects in the tricritical Ising model
• Two-dimensional Anomaly, Orbifolding, and Boundary States
• $3d$ One-form Mixed Anomaly and Entanglement Entropy
• Entanglement Entropy and Duality
• Boundary States and Anomalous Symmetries of Fermionic Minimal Models
• 3d Large $N$ Vector Models at the Boundary
• Precise lower bound on Monster brane boundary entropy

Cited by in corpus (7)

• Fermionization of fusion category symmetries in 1+1 dimensions
• Boson-fermion duality with subsystem symmetry
• Crosscap States in Integrable Field Theories and Spin Chains
• Parity and Spin CFT with boundaries and defects
• Boundary conditions and anomalies of conformal field theories in 1+1 dimensions
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Information metric on the boundary