Duality, generalized Chern-Simons terms and gauge transformations in a high-dimensional curved spacetime

TL;DR

This paper explores duality in high-dimensional curved spacetimes, introducing new gauge transformations that connect electric-magnetic duality with Chern-Simons terms, expanding understanding of gauge theories in complex geometries.

Contribution

It presents two dual formulations involving currents and Chern-Simons terms in arbitrary odd dimensions, with a novel gauge transformation framework for curved spacetimes.

Findings

Two dual worlds with different field contents are constructed.

A new gauge transformation form is introduced for curved spacetimes.

The framework accommodates magnetic monopoles and generalized Chern-Simons terms.

Abstract

With two typical parent actions we have two kinds of dual worlds: i) one of which contains an electric as well as magnetic current, and ii) the other contains (generalized) Chern-Simons terms. All these fields are defined on a curved spacetime of arbitrary (odd) dimensions. A new form of gauge transformations is introduced and plays an essential role in defining the interaction with a magnetic monopole or in defining the generalized Chern-Simons terms.