Non-associative differential geometry and L algebras towards a description of non-geometric closed string vacua
Lead Research Organisation:
Heriot-Watt University
Department Name: S of Mathematical and Computer Sciences
Abstract
The foundations of a non-associative gravity induced by locally non-geometric R-flux backgrounds of string theory were laid in [1]. Moving on the same direction, we study the relation of invariance under non-associative diffeomorphisms on spacetime of our geometry, the classical diffeomorphism symmetry of closed string theory and the generalized diffeomorphism symmetries of double field theory. Furthermore, we aim to construct an appropriate action functional for the on-associative Einstein equations, and further study the pullbacks of phase space Torsion and Riemann curvatures to the underlying spacetime. Towards this goal we shall express Einstein-Cartan gravity in the language of L algebras, as done recently for usual gauge theories [2]. Following that, we aim to twist the underlying geometrical structure. This line of research should provide evidence for the expected relevance of non associative geometry as a low energy limit of closed string theory
Organisations
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509474/1 | 01/10/2016 | 30/09/2021 | |||
| 2127822 | Studentship | EP/N509474/1 | 01/10/2017 | 30/09/2021 | Grigorios Giotopoulos |
| Description | At the current stage, the data governing Einstein's theory of gravity in any dimension have been encoded in the algebraic language of Lie - infinity algebras. Relations to topological theories such as Chern Simons and BF in 3 dimensions have been studied. The paper included the above will be published the coming days. Furthermore, using the framework of L - infinity algebras I have been able to consistently deform gravity to a new non commutative version. This new deformation consistently deforms the kinematical data, dynamics, gauge symmetries and Noether identities of the theory. These results will be published after the first paper is out. |
| Exploitation Route | The procedure for deforming existing theories will be generalised and a framework will be laid out for any theoretical physicist to readily use to deform an existing theory due to non commutative and non associative deformations of spacetime. In principle, albeit for energy constraints, new predictions will be calculable. |
| Sectors | Other |