Note on the self-duality of gauge fields in topologically nontrivial spacetime

TL;DR

This paper derives the self-duality relation for abelian higher-form gauge fields in topologically nontrivial spacetimes by introducing a new gauge transformation, extending previous methods limited to trivial topologies.

Contribution

It presents a novel gauge transformation that allows deriving self-duality relations in nontrivial topological backgrounds, broadening the applicability of existing theories.

Findings

New gauge transformation enables self-duality derivation in nontrivial topology

Extends Pasti-Sorokin-Tonin action to topologically complex spacetimes

Provides a method for analyzing gauge fields in nontrivial topological settings

Abstract

We show the derivation of the self-duality relation of abelian higher-form gauge field strength in the topologically nontrivial spacetime background. The so-called Pasti-Sorokin-Tonin action for the self-dual abelian gauge field assumes that the spacetime topology is trivial to derive the self-duality relation using a gauge transformation of the action. In this paper we find a new gauge transformation of the same theory and show that this new gauge transformation enables us to derive the self-duality relation even in the topologically nontrivial spacetime background.