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arXiv · hep-th/0007019

Non-Linear Electrodynamics in Curved Backgrounds

Gary W. Gibbons·Koji Hashimoto
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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.

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Gary W. Gibbons, Koji Hashimoto. 2000-11-15. Non-Linear Electrodynamics in Curved Backgrounds. https://doi.org/10.1088/1126-6708%2F2000%2F09%2F013

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