Abstract
We study a supersymmetry breaking deformation of the mathcal{N}=left(2,2right) 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.
Highlights
JHEP07(2018)059 duality and couple this to a background vector multiplet
We will show that the cigar theory flows to the massive Thirring model, while the Liouville theory becomes Sine-Gordon
There is a natural non-supersymmetric analog of the Hori-Kapustin mirror pair: FZZ duality [7]. This is an equivalence between the bosonic cigar and sine-Liouville theory, proven in [8]
Summary
Turning on scalar and D-term parameters in this vector multiplet allows us to map supersymmetry breaking deformations across the duality. (Note that we refer to superspace coordinates as θ to avoid confusion with the Sine-Gordon scalar θ that will make an appearance later.) The background gauge field Ai, with field strength F01, couples to the U(1)V current; we will have need for this when we come to compare the symmetries across the duality. As in the cigar theory, we couple this current to a background superfield V .
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