A Short Review on the Bosonization Duality in 2+1D Chern-Simons-Matter Theories

Abstract

This review discusses Bose-Fermi dualities in 2+1 dimensional Chern-Simons-matter theories, focusing on the conjecture that free (regular) fermions coupled to a Chern-Simons gauge field are level-rank dual to Chern-Simons gauged critical (Wilson-Fisher) bosons. In the bosonic theory, the sign of the mass deformation determines whether the system enters a Higgsed (condensed) or unHiggsed (uncondensed) phase. We review large-N computations of the thermal free energy in both phases of the bosonic theory and explore how these results align with their fermionic counterparts under the proposed duality. Notably, this mapping reveals a striking feature : in the unHiggsed phase, the fermions are dual to fundamental scalar excitations, while in the Higgsed phase, the same fermionic degrees of freedom map onto massive W-bosons.