Correlator-Level Verification of Mass and Current Maps in Abelian Chern-Simons Dualities

TL;DR

This paper provides a direct verification of Abelian Chern-Simons dualities at the correlator level by constructing explicit operator realizations and examining mass and current maps in three-dimensional theories.

Contribution

It introduces an explicit local operator realization that reproduces fermion correlation functions and verifies key duality features directly at the correlation function level.

Findings

The predicted relation between bosonic and fermionic mass deformations is quantitatively realized.

The fermionic U(1) current matches the topological gauge current at the infrared fixed point.

Provides correlator-level verification beyond phase structure and anomaly arguments.

Abstract

We construct an explicit local operator realization that reproduces Dirac fermion correlation functions in three spacetime dimensions within an Abelian Chern-Simons framework and use it to examine the conjectured operator and deformation maps of fermion-boson duality directly at the level of correlation functions. We show that the predicted relation between bosonic and fermionic mass deformations, including the relative sign, is realized quantitatively, and that the fermionic U(1) current coincides with the topological gauge current inside correlation functions at the infrared fixed point. These results provide a direct correlator-level verification of key features of Abelian Chern-Simons dualities, going beyond arguments based solely on phase structure, anomaly matching, or large-N considerations.