Electric-magnetic duality beyond four dimensions and in general Relativity

TL;DR

This paper explores the extension of electric-magnetic duality to higher dimensions and in general relativity, introduces a new gravitational instanton equation, and reveals a novel linearized duality in de Sitter space.

Contribution

It generalizes duality concepts beyond four dimensions and in gravity, and presents new results on gravitational instantons and duality in de Sitter space.

Findings

Generalized duality to arbitrary dimensions and p-form fields

Introduced a new exact gravitational instanton equation

Discovered a surprising linearized duality in de Sitter space

Abstract

After reviewing briefly the classical examples of duality in four dimensional field theory we present a generalisation to arbitrary dimensions and to p-form fields. Then we explain how U-duality may become part of a larger non abelian V-symmetry in superstring/supergravity theories. And finally we discuss two new results for 4d gravity theory with a cosmological constant: a new exact gravitational instanton equation and a surprizing linearized classical duality around de Sitter space.