Abstract
Three dimensional bosonization is a conjectured duality between non-super-symmetric 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 \( \mathcal{N}=2 \) 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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Gur-Ari, G., Yacoby, R. Three dimensional bosonization from supersymmetry. J. High Energ. Phys. 2015, 13 (2015). https://doi.org/10.1007/JHEP11(2015)013
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DOI: https://doi.org/10.1007/JHEP11(2015)013