On the duality of three-dimensional superfield theories

TL;DR

This paper explores the duality between supersymmetric Maxwell-Chern-Simons and self-dual theories in three dimensions, highlighting the complexities of dualizing matter-coupled models and confirming duality at quantum levels.

Contribution

It constructs a dual theory to the self-dual model with matter, revealing a more complex gauge structure and analyzing duality beyond classical approximation.

Findings

Duality holds at the tree level.

Dual theory has restricted gauge invariance.

Duality persists at lowest order quantum corrections.

Abstract

Within the superfield approach, we consider the duality between the supersymmetric Maxwell-Chern-Simons and self-dual theories in three spacetime dimensions. Using a gauge embedding method, we construct the dual theory to the self-dual model interacting with a matter superfield, which turns out to be not the Maxwell-Chern-Simons theory coupled to matter, but a more complicated model, with a ``restricted'' gauge invariance. We stress the difficulties in dualizing the self-dual field coupled to matter into a theory with complete gauge invariance. After that, we show that the duality, achieved between these two models at the tree level, also holds up to the lowest order quantum corrections.