Three Dimensional Bosonization From Supersymmetry

TL;DR

The paper demonstrates that non-supersymmetric three-dimensional bosonization can be derived from the well-established ${ m N}=2$ Giveon-Kutasov duality. By employing a double-trace flow to an IR fixed point where scalars and fermions decouple in the planar limit, the authors show that planar correlators of single-trace operators in the bosonic and fermionic theories match, and they derive the complete duality map for the most general renormalizable potential $V(ar{oldsymbol heta}oldsymbol heta)$ in theories with both a scalar and a fermion. They provide two complementary routes: perturbation theory in the ${ m N}=2$ multi-trace couplings and a double-trace flow combined with background-field techniques, both avoiding explicit planar diagram computations. The work yields precise operator and coupling correspondences, including new signs in the current mappings, and offers a framework to extend bosonization to all planar correlators, with potential implications for finite-$N$ extensions and holographic dual descriptions.

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.

Figures (3)

• Figure 1: A generic planar contribution to $\langle O_b O_f \rangle_\mathcal{T}$. Dashed lines represent scalar propagators, solid lines represent fermion propagators, and crosses denote the operator insertions.
• Figure 2: A generic planar contribution to $\langle O_b O_b \rangle_\mathcal{T}$. The notation is the same as in Figure \ref{['fig:ObOf']}.
• Figure 3: Planar diagrams contributing to the 4-point function of bosonic spin-1 currents in the $\mathcal{N}=2$ theory. The notation is the same as in Figure \ref{['fig:ObOf']}.