Fermionization of conformal boundary states

TL;DR

This work addresses how to classify boundary states in two-dimensional fermionic CFTs by leveraging the known bosonic boundary data. It employs $\Z_2$ defect lines to realize orbifold and fermionization operations, yielding two mutually incompatible groups of fermionic boundary conditions distinguished by $\, obreak\sqrt{2}$-multipliers in the open-channel spectrum. The authors provide explicit constructions and consistency checks for boundary states across the original (A-type), orbifold (D-type), and fermionic (F and tilde F) theories, including NS and R sector details and GSO-like projections. The results illuminate how dualities and defect-based formalisms reshuffle boundary data, with potential implications for entanglement entropy, anomaly analysis, and lattice realizations of fermionic BCFTs. Overall, the paper delivers a complete enumeration of elementary boundary states in 2D fermionic CFTs and clarifies the interplay between boundary conditions, dualities, and Majorana zero modes.

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.