Classical Duality from dimensional reduction of Self Dual 4-form Maxwell Theory in 10 dimensions

TL;DR

This paper explores how duality symmetries in 4-dimensional gauge theories can be derived from the dimensional reduction of a 10-dimensional self-dual 4-form Maxwell theory, linking duality to the geometry of compactification.

Contribution

It provides a geometric understanding of duality generators in 4D gauge theories via dimensional reduction of a 10D self-dual 4-form theory, highlighting the role of compact space geometry.

Findings

Duality generators are derived from compactification geometry.

The reduced theory includes scalar, one-form, and two-form fields.

Duality acts non-trivially on all fields in the reduced theory.

Abstract

By dimensional reduction of a self dual p-form theory on some compact space, we determine the duality generators of the gauge theory in 4 dimensions. In this picture duality is seen as a consequence of the geometry of the compact space. We describe the dimensional reduction of 10-dimensional self dual 4-form Maxwell theory to give a theory in 4-dimensions with scalar, one form and two form fields that all transform non trivially under duality.