A Note on E11 and Three-dimensional Gauged Supergravity
Eric A. Bergshoeff, Olaf Hohm, Teake A. Nutma
TL;DR
This paper analyzes the gauge symmetries in three-dimensional gauged supergravity, showing their relation to the E11 algebra and highlighting the role of dynamics in symmetry closure.
Contribution
It explicitly determines gauge symmetries of p-forms in maximal 3D gauged supergravity and connects them to E11 predictions, emphasizing on-shell closure.
Findings
Gauge symmetries match E11 predictions in ungauged limit
Closure of gauge algebra is off-shell in ungauged case
Closure becomes on-shell in the gauged theory
Abstract
We determine the gauge symmetries of all p-forms in maximal three-dimensional gauged supergravity by requiring invariance of the Lagrangian. It is shown that in a particular ungauged limit these symmetries are in precise correspondence to those predicted by the very-extended Kac-Moody algebra E11. We demonstrate that whereas in the ungauged limit the bosonic gauge algebra closes off-shell, the closure is only on-shell in the full gauged theory. This underlines the importance of dynamics for understanding the Kac-Moody origin of the symmetries of gauged supergravity.
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