Constitutive relations, off shell duality rotations and the hypergeometric form of Born-Infeld theory

Abstract

We review equivalent formulations of nonlinear and higher derivatives theories of electromagnetism exhibiting electric-magnetic duality rotations symmetry. We study in particular on shell and off shell formulations of this symmetry, at the level of action functionals as well as of equations of motion. We prove the conjecture that the action functional leading to Born-Infeld nonlinear electromagnetism, that is duality rotation invariant off shell and that is known to be a root of an algebraic equation of fourth order, is a hypergeometric function.

20 pages. Contribution to the proceedings of the conference BUDS2013, Frascati

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• Self-duality, helicity conservation and normal ordering in nonlinear QED
• Two-Field Born-Infeld with Diverse Dualities
• Self-duality for $\mathcal{N}$-extended superconformal gauge multiplets
• Majorana Fermions, Supersymmetry Breaking, and Born-Infeld Theory