Bose-Fermi Chern-Simons Dualities in the Higgsed Phase

TL;DR

This paper verifies the Bose-Fermi Chern-Simons duality in the Higgsed phase by matching the thermal free energies of the condensed bosonic and fermionic theories at large N, extending previous checks to negative mass deformations.

Contribution

It provides an all-orders large N calculation of the thermal free energy in the Higgsed phase, confirming the duality for negative mass deformations.

Findings

Matching free energies for bosonic and fermionic theories in the Higgsed phase.

Confirmation of duality beyond positive mass deformations.

Explicit large N results involving W bosons.

Abstract

It has been conjectured that fermions minimally coupled to a Chern-Simons gauge field define a conformal field theory (CFT) that is level-rank dual to Chern-Simons gauged Wilson-Fisher Bosons. The CFTs in question admit relevant deformations parametrized by a real mass. When the mass deformation is positive, the duality of the two deformed theories has previously been checked in detail in the large $N$ limit by comparing explicit all orders results on both sides of the duality. In this paper we perform a similar check for the case of negative mass deformations. In this case the bosonic field condenses triggering the Higgs mechanism. The effective excitations in this phase are massive $W$ bosons. By summing all leading large $N$ graphs involving these $W$ bosons we find an all orders (in the 't Hooft coupling) result for the thermal free energy of the bosonic theory in the condensed phase. Our final answer perfectly matches the previously obtained fermionic free energy under the conjectured duality map.