Bosonization and Mirror Symmetry

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.

24 pages, 2 figures, 1 appendix

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Cited by in corpus (9)

• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• Duality between the deconfined quantum-critical point and the bosonic topological transition
• Nonsupersymmetric dualities from mirror symmetry
• Composite fermion duality for half-filled multicomponent Landau Levels
• Embedding three-dimensional bosonization dualities into string theory
• Quantum phase transition in many-flavor supersymmetric QED${}_3$
• Two-dimensional conductors with interactions and disorder from particle-vortex duality
• Conformal field theory and the hot phase of three-dimensional U(1) gauge theory
• Discussion of the Duality in Three Dimensional Quantum Field Theory