On the coupling of the self-dual field to dynamical U(1) Matter and its dual theory

TL;DR

This paper explores the classical and quantum duality between a self-dual field coupled to U(1) charged matter and a Maxwell Chern-Simons type theory, highlighting conditions for quantum equivalence.

Contribution

It derives a dual Maxwell Chern-Simons model for a general non-minimal coupling and clarifies when quantum equivalence holds without extra terms.

Findings

Classical equivalence between self-dual and Maxwell Chern-Simons theories.

Quantum equivalence depends on the linearity of the coupling.

Extra terms are needed at quantum level for general couplings.

Abstract

We consider an arbitrary U(1) charged matter non-minimally coupled to the self-dual field in $d=2+1$. The coupling includes a linear and a rather general quadratic term in the self-dual field. By using both a Lagragian gauge embedding and a master action approaches we derive the dual Maxwell Chern-Simons type model and show the classical equivalence between the two theories. At quantum level the master action approach in general requires the addition of an awkward extra term to the Maxwell Chern-Simons type theory. Only in the case of a linear coupling in the self-dual field the extra term can be dropped and we are able to establish the quantum equivalence of gauge invariant correlation functions in both theories.