Mirror Symmetry and Bosonization in 2d and 3d

Abstract

We study a supersymmetry breaking deformation of the 2d N=(2,2) cigar=Liouville mirror pair, first introduced by Hori and Kapustin. We show that mirror symmetry flows in the infra-red to 2d bosonization, with the theories reducing to massive Thirring and Sine-Gordon respectively. The exact bosonization map emerges at one-loop. We further compactify non-supersymmetric 3d bosonization dualities on a circle and argue that these too flow to 2d bosonization at long distances.

arXiv comment13 pages. v2: addendum on emergence of Z2 gauge fields upon compactification

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Cited by in corpus (15)

• A Web of 2d Dualities: ${\mathbf{Z}}_2$ Gauge Fields and Arf Invariants
• Duality between $(2+1)d$ Quantum Critical Points
• An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
• Evidence for a Non-Supersymmetric 5d CFT from Deformations of 5d $SU(2)$ SYM
• 3d-3d correspondence for mapping tori
• Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• Fermi seas from Bose condensates in Chern-Simons matter theories and a bosonic exclusion principle
• The large $N$ phase diagram of $\mathcal{N}=2$ $SU(N)$ Chern-Simons theory with one fundamental chiral multiplet
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• The Hilbert Space of large $N$ Chern-Simons matter theories
• Lattice Construction of Duality with Non-Abelian Gauge Fields in 2+1D
• On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter
• Fermion-fermion duality in 3+1 dimensions
• Singular BPS boundary conditions in $\mathcal{N}=(2,2)$ supersymmetric gauge theories