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.
Extended geometry and gauged maximal supergravity
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abstract
We consider generalized diffeomorphisms on an extended mega-space associated to the U-duality group of gauged maximal supergravity in four dimensions, E_7. Through the bein for the extended metric we derive dynamical (field-dependent) fluxes taking values in the representations allowed by supersymmetry, and obtain their quadratic constraints from gauge consistency conditions. A covariant generalized Ricci tensor is introduced, defined in terms of a connection for the generalized diffeomorphisms. We show that for any torsionless and metric-compatible generalized connection, the Ricci scalar reproduces the scalar potential of gauged maximal supergravity. We comment on how these results extend to other groups and dimensions.
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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.