New Geometries for Gravity and Spacetime

Project Summary

Reconciling general relativity and quantum mechanics and understanding the quantum structure of spacetime is one of the major challenges for present day theoretical physics. Two prominent frameworks addressing this conundrum are string theory and noncommutative geometry. Recent advances provide evidence that the generic spacetime geometries experienced by closed strings are noncommutative and even nonassociative.

Within this project we aim at a deeper understanding of the geometry and the gravitational sector of string theory. In particular, we are going to study strings propagating in backgrounds with non-geometric fluxes, using mathematical tools such as noncommutative and nonassociative differential geometry, Courant algebroids, generalized and higher geometry. Our main goal is to provide a solid geometric basis for T- and U-duality-invariant theories, such as double field theory and exceptional field theories, elucidate the structure of string and membrane sigma models, construct models of gravity in the presence of general fluxes and brane sources and study their physical implications. A second goal is to investigate the geometric structure of non-relativistic gravity theories, which attract a lot of interest in recent years due to applications in diverse physical settings, ranging from holography and condensed matter physics to string theory.

We expect that the results of this project will have an impact in our understanding of the gravitational interaction, and will contribute to the long-term goal of elucidating the origin and the structure of the universe.