Chern Simons Bosonization along RG Flows

TL;DR

This paper investigates the duality between bosonic and fermionic theories coupled to Chern-Simons gauge fields along RG flows, showing exact agreement of thermal partition functions and proposing a duality map connecting these flows from UV to IR.

Contribution

It provides a detailed analysis of RG flows between dual Chern-Simons matter theories and conjectures a precise duality map extending the bosonization correspondence along these flows.

Findings

Exact matching of thermal partition functions along RG flows.

Proposal of a duality map relating bosonic and fermionic theories.

RG flows can be tuned to connect free bosonic and fermionic fixed points.

Abstract

It has previously been conjectured that the theory of free fundamental scalars minimally coupled to a Chern Simons gauge field is dual to the theory of critical fundamental fermions minimally coupled to a level rank dual Chern Simons gauge field. In this paper we study RG flows away from these two fixed points by turning on relevant operators. In the t' Hooft large N limit we compute the thermal partition along each of these flows and find a map of parameters under which the two partition functions agree exactly with each other all the way from the UV to the IR. We conjecture that the bosonic and fermionic RG flows are dual to each other under this map of parameters. Our flows can be tuned to end at the gauged critical scalar theory and gauged free fermionic theories respectively. Assuming the validity of our conjecture, this tuned trajectory may be viewed as RG flow from the gauged theory of free bosons to the gauged theory of free fermions.