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.
Highlights
Bosonization is a duality that equates a fermionic description of a particular system to an alternative bosonic one
Because theory A is free, the effects of the deformations we consider are understood: we show that there exist two distinct massive phases in a particular parameter regime that are separated by a single critical point whose lagrangian description is that of a free Dirac fermion, i.e., the left-hand side of (1.4)
We focus on one example of this duality
Summary
Bosonization is a duality that equates a fermionic description of a particular system to an alternative bosonic one. The direct demonstration for the duality constructs the Dirac fermion from a coherent state of bosons [4]. This duality has had incredible utility for the description of 1+1D condensed matter systems that range from spin models and itinerant fermions to the excitations living on the edges of quantum Hall droplets [5, 6]. There has been substantial progress in motivating a large class of new bosonization dualities [7,8,9]. Aharony [10] (see [11, 12]) has clarified the basic structure of these conjectured dualities (indicated by ↔): Nf fermions coupled to.
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