Fermionization and boundary states in 1+1 dimensions

TL;DR

This paper explores how boundary states in 1+1 dimensional fermionic theories correspond to those in bosonic theories via Jordan-Wigner transformations, interpreting the mapping as fusion with a fermionization interface.

Contribution

It explicitly determines the mapping of boundary states under fermionization and interprets this as a fusion process, advancing understanding of boundary conditions in fermionic-bosonic dualities.

Findings

Boundary states are mapped explicitly under fermionization.

The mapping is interpreted as fusion with a fermionization interface.

Provides a framework for analyzing boundary conditions in 1+1D fermionic theories.

Abstract

In the last few years it was realized that every fermionic theory in 1+1 dimensions is a generalized Jordan-Wigner transform of a bosonic theory with a non-anomalous $\mathbb{Z}_2$ symmetry. In this note we determine how the boundary states are mapped under this correspondence. We also interpret this mapping as the fusion of the original boundary with the fermionization interface.