Three Dimensional Bosonization From Supersymmetry

TL;DR

This paper proves the validity of three-dimensional bosonization duality for non-supersymmetric theories by leveraging supersymmetric duality and double-trace flows, avoiding explicit diagram calculations.

Contribution

It demonstrates that non-supersymmetric bosonization holds for all planar correlators by deriving it from supersymmetric duality via double-trace flows.

Findings

Bosonization duality is valid for all planar correlators.

The proof does not require explicit planar diagram computations.

The technique generalizes to duality mappings of all renormalizable couplings.

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.