Sp(2n,R) electric-magnetic duality as off-shell symmetry of interacting electromagnetic and scalar fields

Abstract

It was established long ago that SO(2) electric-magnetic duality is an {\em off-shell} symmetry of the free Maxwell theory, i.e., that it leaves invariant the action and not just the equations of motion. We review here that analysis and extend it to the Maxwell field coupled to scalar fields defined on the $SL(2,\mathbb{R})/SO(2)$ coset space, showing that $SL(2,\mathbb{R})$ is in that case an {\em off-shell} symmetry. We also show how the result can be generalized to many Maxwell fields and $Sp(2n,\mathbb{R})$ duality symmetry - or a subgroup of it, recovering in particular the case of maximal supergravity in four dimensions with $E_{7,7}$ symmetry. We finally indicate further possible extensions to twisted self-duality equations for $p$-forms, including Chern-Simons terms and Pauli couplings, as well as linearized gravity, which will be treated in depth elsewhere.

Published in Quarks, Strings and the Cosmos - Héctor Rubinstein Memorial Symposium (Proceedings of Science) - Minor typos corrected

References in corpus (4)

• E7(7) symmetry in perturbatively quantised N=8 supergravity
• E7(7) invariant Lagrangian of d=4 N=8 supergravity
• Can (Electric-Magnetic) Duality Be Gauged?
• Local electromagnetic duality and gauge invariance

Cited by in corpus (6)

• E{7(7)} Symmetry and Finiteness of N=8 Supergravity
• The Action for Twisted Self-Duality
• Gravitational Electric-Magnetic Duality, Gauge Invariance and Twisted Self-Duality
• Can (Electric-Magnetic) Duality Be Gauged?
• Deformations of vector-scalar models
• Supersymmetric electric-magnetic duality as a manifest symmetry of the action for super-Maxwell theory and linearized supergravity