The emergence of hidden symmetries in gravitational theories is an intriguing phenomenon. The toroidal compactication of eleven dimensional supergravity on a (11 D)-torus yields maximally extended supergravity in dimension Dwith a symmetry structure hidden within the non-gravitational part of the reduced bosonic sector. In pure gravity, the compactication of the four-dimensional theory to three and two dimensions yields as hidden symmetries the Ehlers group and the Geroch group, respectively. These results have motivated the conjecture that some indefinite Kac-Moody algebra might be a fundamental symmetry of gravitational theories. Further evidence in favor of this conjecture has been collected from the study of the billiard reformulation of the BKL chaotic dynamics near a cosmological singularity in gravity and supergravity models: the indefinite Kac-Moody algebra structure is encoded within the billiard walls, the billiard motion taking place in its fundamental Weyl chamber.
These indefinite Kac-Moody algebras contain on an equal footing fields and their Hodge duals, including the graviton. In four dimensions, the graviton and its dual field are both symmetric tensors, and it is expected that a gravitational duality relating them may be inherited from the Kac-Moody algebra structure.
The aim of the project is twofold:
i) to study duality in gravity and higher spin theories in cosmological scenarios, including the AdS background and possible connections with a holographic conjecture relating the action of duality on the bulk to transformations of two-point functions in the boundary.
ii) to investigate whether the billiard reformulation of the BKL dynamics, in particular the hidden Kac-Moody structure encoded within the billiard walls, can be of use in generalizing the notion of holographic complexity to non-AdS scenarios.
|Sergio Hörtner||University of Amsterdam|