Abstract
We present a systematic study of nonlinear and higher derivatives extensions of electromagnetism. We clarify when action functionals S[F] can be explicitly obtained from arbitrary (not necessarily self-dual) nonlinear equations of motion. We show that the “Deformed twisted self-duality condition” proposal originated in the context of supergravity counterterms is actually the general framework needed to discuss self-dual theories starting from a variational principle.
We generalize to nonlinear and higher derivatives theories Schrödinger formulation of Born-Infeld theory, and for the latter, and more in general for nonlinear theories, we derive a closed form expression of the corresponding deformed twisted self-duality conditions. This implies that the hypergeometric expression entering these duality conditions and leading to Born-Infeld theory satisfies a hidden quartic equation.
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P. Aschieri and S. Ferrara, unpublished (Oct. 2012).
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ArXiv ePrint: 1302.4737
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Aschieri, P., Ferrara, S. Constitutive relations and Schrödinger’s formulation of nonlinear electromagnetic theories. J. High Energ. Phys. 2013, 87 (2013). https://doi.org/10.1007/JHEP05(2013)087
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DOI: https://doi.org/10.1007/JHEP05(2013)087