Constitutive relations and Schroedinger's formulation of nonlinear electromagnetic theories

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 Schroedinger 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.

Revised version with: integrability conditions on equations of motion; equivalence between deformed twisted self-duality conditions and equations of motion from action functionals S[F] (Section 2.5); stressed universality of the quartic equation. References added. 31 pages. To appear in JHEP

References in corpus (5)

• E7(7) constraints on counterterms in N=8 supergravity
• Stringy KLT relations, global symmetries, and E_7(7) violation
• On duality symmetries of supergravity invariants
• N=8 Counterterms and E7(7) Current Conservation
• Duality rotations in supersymmetric nonlinear electrodynamics revisited

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• Two-Field Born-Infeld with Diverse Dualities
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