Fermionization of conformal boundary states

TL;DR

This paper constructs all boundary states in 2D fermionic conformal field theories from their bosonic counterparts, revealing two incompatible boundary condition groups linked to Majorana zero modes and discussing implications for entanglement entropy.

Contribution

It provides a complete classification of fermionic boundary states derived from bosonic models, highlighting the role of Majorana zero modes and boundary condition incompatibility.

Findings

Two groups of boundary conditions with distinct partition function contributions

Identification of Majorana zero modes through the  coefficient

Incompatibility of the two boundary condition groups

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.