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arXiv · 1507.04378

Three Dimensional Bosonization From Supersymmetry

Guy Gur-Ari·Ran Yacoby
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Abstract

Three dimensional bosonization is a conjectured duality between non-supersymmetric Chern-Simons theories coupled to matter fields in the fundamental representation of the gauge group. There is a well-established supersymmetric version of this duality, which involves Chern-Simons theories with ${\cal N} = 2$ supersymmetry coupled to fundamental chiral multiplets. Assuming that the supersymmetric duality is valid, we prove that non-supersymmetric bosonization holds for all planar correlators of single-trace operators. The main tool we employ is a double-trace flow from the supersymmetric theory to an IR fixed point, in which the scalars and fermions are effectively decoupled in the planar limit. A generalization of this technique can be used to derive the duality mapping of all renormalizable couplings, in non-supersymmetric theories with both a scalar and a fermion. Our results do not rely on an explicit computation of planar diagrams.

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Guy Gur-Ari, Ran Yacoby. 2015-07-15. Three Dimensional Bosonization From Supersymmetry. https://arxiv.org/abs/1507.04378

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