Aspects of Space-Time Dualities

TL;DR

This paper explores space-time dualities in Abelian gauge theories, examining their geometric interpretations via compactifications of self-dual forms in higher dimensions and their connections to superstring theories.

Contribution

It introduces a novel perspective on duality groups as geometric symmetries in higher-dimensional theories and relates these to string theory compactifications.

Findings

Duality groups include transformations relating different space-times.

Compactifications of self-dual forms connect to superstring theories.

Geometric interpretations of dualities are established in higher dimensions.

Abstract

Duality groups of Abelian gauge theories on four manifolds and their reduction to two dimensions are considered. The duality groups include elements that relate different space-times in addition to relating different gauge-coupling matrices. We interpret (some of) such dualities as the geometrical symmetries of compactified theories in higher dimensions. In particular, we consider compactifications of a (self-dual) 2-form in 6-D, and compactifications of a self-dual 4-form in 10-D. Relations with a self-dual superstring in 6-D and with the type IIB superstring are discussed.