Non-linear electrodynamics in curved backgrounds

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)×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 Kähler manifolds and Schwarzshild black holes with a b-field.

Almost Product Manifolds as the Low Energy Geometry of Dirichlet Branes

“…Indices µ, ν are lifted and lowered using the induced metric on the brane. Note that (1) can be viewed as a theory of non-linear electrodynamics [6], and has in fact been devised as such in the 1930s [7] in order to covariantly regularize the energy divergence of the electrostatic field of a charged point particle in Maxwell theory. Expansion of the determinant, using the identity det(1 + F ) = exp tr ln(1 + F ), with F = B + 2 F , shows that only even powers of F contribute to the action.…”

4D, N = 1 Born-Infeld supergravity

“…In four dimensions, the BR tensor (3.13) can be identically rewritten to 14) whereR mspt is the dual curvature. Moreover, in four dimensions the BR tensor is known to be symmetric in all four indices and pairwise traceless [20].…”

“…[13,14] for earlier discussions without supersymmetry). A supersymmetric BI action possesses more physically important features when compared to its purely bosonic BI part (e.g.…”

“…Of course, one could simply extend the determinantal prescription by using the most general substitution under the square root of the determinant, viz. 14) where X µν is any tensor quadratic or higher in the full curvature, and ζ is yet another dimensional constant [13]. Unfortunately, all these prescriptions do not have natural supersymmetric extensions and, therefore, they are ignored in what follows.…”

Nonlinear self-duality and supersymmetry

“…The theory can be equivalently represented in the form 24) where the complex field χ is a functions of U andṼ which satisfies the nonlinear constraint…”