Duality Rotations in Nonlinear Electrodynamics and in Extended Supergravity

TL;DR

This paper reviews duality rotations in nonlinear electrodynamics and supergravity, establishing conditions for duality symmetry, with examples like Born-Infeld theory and exploring their role in N=2 supergravity.

Contribution

It provides a comprehensive overview of duality rotations, their conditions for symmetry, and their application in supergravity, highlighting the geometric connection with special Kähler manifolds.

Findings

Born-Infeld theory exhibits Sp(2n,R) self-duality.

Duality rotations are crucial in formulating N=2 supergravity.

Conditions for duality symmetry are explicitly established.

Abstract

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.