On the coupling of the self-dual field to dynamicalU(1) matter and its dual theory

Abstract

We consider 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 Lagragian gauge embedding and master action approaches we derive the dual Maxwell Chern–Simons-type model and show the classical equivalence between the two theories. At the 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 can the extra term be dropped and we are able to establish the quantum equivalence of gauge invariant correlation functions in both theories.