Quantum equivalence between the self-dual and the Maxwell-Chern-Simons models nonlinearly coupled to U(1) scalar fields

TL;DR

This paper demonstrates quantum duality between the self-dual and Maxwell-Chern-Simons models coupled to U(1) scalar fields, overcoming nonlinear interaction complexities through perturbative integration and effective action analysis.

Contribution

It introduces a method to establish quantum duality in nonlinear coupled models by perturbative integration, avoiding complications of master action approaches.

Findings

Duality holds for partition functions and some correlation functions.

Effective actions can be derived up to cubic coupling terms.

Restrictions on scalar field coupling ensure ghost-free theories.

Abstract

The use of master actions to prove duality at quantum level becomes cumbersome if one of the dual fields interacts nonlinearly with other fields. This is the case of the theory considered here consisting of U(1) scalar fields coupled to a self-dual field through a linear and a quadratic term in the self-dual field. Integrating perturbatively over the scalar fields and deriving effective actions for the self-dual and the gauge field we are able to consistently neglect awkward extra terms generated via master action and establish quantum duality up to cubic terms in the coupling constant. The duality holds for the partition function and some correlation functions. The absence of ghosts imposes restrictions on the coupling with the scalar fields.