Generalized duality between local vector theories in $D=2+1$

TL;DR

This paper establishes a new duality between a generalized self-dual model in 2+1 dimensions and a pair of non-interacting Maxwell-Chern-Simons theories, resolving previous issues with nonlocality and ghosts.

Contribution

It introduces a first-order auxiliary field approach to define a master action linking the GSD model to dual Maxwell-Chern-Simons theories with opposite helicities.

Findings

A master action interpolates between GSD and dual MCS theories.

The dual gauge theory involves doubled fields due to an auxiliary field.

Gauge-invariant correlators can be derived between models.

Abstract

The existence of an interpolating master action does not guarantee the same spectrum for the interpolated dual theories. In the specific case of a generalized self-dual (GSD) model defined as the addition of the Maxwell term to the self-dual model in $D=2+1$, previous master actions have furnished a dual gauge theory which is either nonlocal or contains a ghost mode. Here we show that by reducing the Maxwell term to first order by means of an auxiliary field we are able to define a master action which interpolates between the GSD model and a couple of non-interacting Maxwell-Chern-Simons theories of opposite helicities. The presence of an auxiliary field explains the doubling of fields in the dual gauge theory. A generalized duality transformation is defined and both models can be interpreted as self-dual models. Furthermore, it is shown how to obtain the gauge invariant correlators of the non-interacting MCS theories from the correlators of the self-dual field in the GSD model and vice-versa. The derivation of the non-interacting MCS theories from the GSD model, as presented here, works in the opposite direction of the soldering approach.