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Duality rotations in nonlinear electrodynamics and in extended supergravity

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We review the general theory of duality rotations which, in four dimensions, exchange electric with magnetic fields. Necessary and sufficient conditions in order for a theory to have duality symmetry are established. A nontrivial example is Born-Infeld theory with n Abelian gauge fields and with Sp(2n, ℝ) self-duality. We then review duality symmetry in supergravity theories. In the case of N = 2 supergravity duality rotations are in general not a symmetry of the theory but a key ingredient in order to formulate the theory itself. This is due to the beautiful relation between the geometry of special Kahler manifolds and duality rotations.

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Authors and Affiliations

  1. Centro Studi e Ricerche “Enrico Fermi”- Compendio Viminale, 00184, Roma, Italy

    P. Aschieri

  2. Dipartimento di Scienze e Tecnologie Avanzate, Universita del Piemonte Orientale e INFN, Sezione di Torino, gruppo collegato di Alessandria, Via Bellini 25/G, 15100, Alessandria, Italy

    P. Aschieri

  3. Physics Department, Theory Unit, CERN, CH 1211, Geneva 23, Switzerland

    S. Ferrara

  4. INFN, Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044, Frascati, Italy

    S. Ferrara

  5. Department of Physics and Astronomy, University of California, Los Angeles, CA, USA

    S. Ferrara

  6. Department of Physics, University of California and Theoretical Physics Group, Bldg. 50A5104, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA

    B. Zumino

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Aschieri, P., Ferrara, S. & Zumino, B. Duality rotations in nonlinear electrodynamics and in extended supergravity. Riv. Nuovo Cim. 31, 625–707 (2008). https://doi.org/10.1393/ncr/i2008-10038-8

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