Three Dimensional Bosonization From Supersymmetry

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 $\mathcal{N}=2$ 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.

39 pages, 3 figures. v2: added references

References in corpus (5)

• Seiberg Duality in Chern-Simons Theory
• Seiberg-like duality in three dimensions for orthogonal gauge groups
• A test of bosonization at the level of four-point functions in Chern-Simons vector models
• Poles in the $S$-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics
• 3D Field Theories with Chern--Simons Term for Large $N$ in the Weyl Gauge