The gauge structure and pseudo-action of extended geometry with ancillary transformations are encoded by a tensor hierarchy algebra S(g+), yielding a partial L-infinity description for finite-dimensional structure groups.
M-theory and Type IIB from a Duality Manifest Action
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abstract
We revisit the SL(5) U-duality manifest action constructed by Berman and Perry in an extended spacetime. Upon choosing a four-dimensional solution to the section condition constraint, the theory reduces to a four-dimensional truncation of eleven-dimensional supergravity. In this paper, we show that the theory contains more than this M-theory reduction. The section condition also admits an SL(5) inequivalent three-dimensional solution, upon which the action directly reduces to a three-dimensional truncation of type IIB supergravity. We also discuss the reduction to IIB$^*$ supergravity.
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Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
The gauge structure and pseudo-action of extended geometry with ancillary transformations are encoded by a tensor hierarchy algebra S(g+), yielding a partial L-infinity description for finite-dimensional structure groups.