Bosonization and Mirror Symmetry

TL;DR

This paper uses mirror symmetry to derive and analyze bosonization dualities in 2+1 dimensions, connecting fermionic and bosonic theories through supersymmetry breaking and gauge couplings.

Contribution

It introduces a supersymmetric framework for deriving bosonization dualities and explores their implications for various known and conjectured dualities in 2+1D.

Findings

Derivation of bosonization duality from mirror symmetry.

Connection of dualities via supersymmetry breaking.

Role of Chern-Simons and BF couplings in dualities.

Abstract

We study bosonization in 2+1 dimensions using mirror symmetry, a duality that relates pairs of supersymmetric theories. Upon breaking supersymmetry in a controlled way, we dynamically obtain the bosonization duality that equates the theory of a free Dirac fermion to QED3 with a single scalar boson. This duality may be used to demonstrate the bosonization duality relating an $O(2)$-symmetric Wilson-Fisher fixed point to QED3 with a single Dirac fermion, Peskin-Dasgupta-Halperin duality, and the recently conjectured duality relating the theory of a free Dirac fermion to fermionic QED3 with a single flavor. Chern-Simons and BF couplings for both dynamical and background gauge fields play a central role in our approach. In the course of our study, we describe a chiral mirror pair that may be viewed as the minimal supersymmetric generalization of the two bosonization dualities.