Duality Rotations in Nonlinear Electrodynamics and in Extended Supergravity

Details Duality Rotations in Nonlinear Electrodynamics and in Extended Supergravity Duality Rotations in Nonlinear Electrodynamics and in Extended Supergravity

2008-07-25

arxiv.org/abs/0807.4039v2

Riv.Nuovo Cim.31:625-708,2009

Physics

High Energy Physics

High Energy Physics - Theory

Invited contribution to Rivista del Nuovo Cimento in occasion of the 2005 Enrico Fermi Prize of the Italian Physical Society.

Scientific paper

10.1393/ncr/i2008-10038-8

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 Kaehler manifolds and duality rotations.

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