Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-01-31
Physics
High Energy Physics
High Energy Physics - Theory
To appear in Quarks, Strings and the Cosmos - H\'ector Rubinstein Memorial Symposium (Proceedings of Science) - Minor typos co
Scientific paper
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.
Bunster Claudio
Henneaux Marc
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