Ghost free dual vector theories in 2+1 dimensions

TL;DR

This paper investigates duality in 2+1 dimensional abelian vector theories, showing that a nonlocal Maxwell-Chern-Simons model can be ghost-free and share the same spectrum as a local generalized self-dual model, with implications for master action methods.

Contribution

It demonstrates how to obtain a ghost-free nonlocal MCS theory dual to a local GSD model using a master action approach, preserving spectrum and duality.

Findings

Both theories have identical spectra and are ghost free.

A new master action connects local GSD to nonlocal MCS models.

Duality persists at quantum level up to contact terms.

Abstract

We explore here the issue of duality versus spectrum equivalence in abelian vector theories in 2+1 dimensions. Specifically we examine a generalized self-dual (GSD) model where a Maxwell term is added to the self-dual model. A gauge embedding procedure applied to the GSD model leads to a Maxwell-Chern-Simons (MCS) theory with higher derivatives. We show that the latter contains a ghost mode contrary to the original GSD model. On the other hand, the same embedding procedure can be applied to $N_f$ fermions minimally coupled to the self-dual model. The dual theory corresponds to $N_f$ fermions with an extra Thirring term coupled to the gauge field via a Pauli-like term. By integrating over the fermions at $N_f\to\infty$ in both matter coupled theories we obtain effective quadratic theories for the corresponding vector fields. On one hand, we have a nonlocal type of the GSD model. On the other hand, we have a nonlocal form of the MCS theory. It turns out that both theories have the same spectrum and are ghost free. By figuring out why we do not have ghosts in this case we are able to suggest a new master action which takes us from the local GSD to a nonlocal MCS model with the same spectrum of the original GSD model and ghost free. Furthermore, there is a dual map between both theories at classical level which survives quantum correlation functions up to contact terms. The remarks made here may be relevant for other applications of the master action approach.