Fermionization of conformal boundary states

Understand

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.