Non-Linear Electrodynamics in Curved Backgrounds

TL;DR

This paper explores non-linear electrodynamics in curved backgrounds, focusing on dualities, topological bounds, and symmetry properties, including dimensional reduction and applications to black hole backgrounds.

Contribution

It establishes topological bounds for self-dual configurations, analyzes duality symmetries in curved space, and introduces a new SO(n) X SO(2) duality-invariant Lagrangian.

Findings

Existence of topological bounds for self-dual Born-Infeld configurations

Vanishing energy-momentum tensor for self-dual solutions

New SO(n) X SO(2) duality-invariant Lagrangian

Abstract

We study non-linear electrodynamics in curved space from the viewpoint of dualities. After establishing the existence of a topological bound for self-dual configurations of Born-Infeld field in curved space, we check that the energy-momentum tensor vanishes. These properties are shown to hold for general duality-invariant non-linear electrodynamics. We give the dimensional reduction of Born-Infeld action to three dimensions in a general curved background admitting a Killing vector. The SO(2) duality symmetry becomes manifest but other symmetries present in flat space are broken, as is U-duality when one couples to gravity. We generalize our arguments on duality to the case of n U(1) gauge fields, and present a new Lagrangian possessing SO(n) X SO(2)_elemag duality symmetry. Other properties of this model such as Legendre duality and enhancement of the symmetry by adding dilaton and axion, are studied. We extend our arguments to include a background b-field in the curved space, and give new examples including almost Kaehler manifolds and Schwarzshild black holes with a $b$-field.