Dualities and models in various dimensions

TL;DR

This paper explores dualities across different dimensions in gauge theories, connecting four-dimensional U(1) theories with theta terms to two-dimensional models, revealing deep relationships through dimensional reduction.

Contribution

It establishes a novel duality between 4D U(1) gauge theories with theta terms and their lower-dimensional counterparts via dimensional reduction.

Findings

Duality between 4D U(1) theories with theta term

Reduction to 3D gauge-scalar theories with monopoles

Connection to 2D QED (Schwinger) model

Abstract

Working within the path-integral framework we first establish a duality between the partion functions of two $U(1)$ gauge theories with a theta term in $d=4$ space-time dimensions. Then, after a dimensional reduction to $d=3$ dimensions we arrive to the partition function of a $U(1)$ gauge theory coupled to a scalar field with an action that exhibits a Dirac monopole solution. A subsequent reduction to $d=2$ dimensions leads to the partition function of a theory in which the gauge field decouples from two scalars which have non-trivial vortex-like solutions. Finally this $d=2$ partition function can be related to the bosonized version of the two-dimensional QED$_2$ (Schwinger) model.