Dual Gravity, Higher Spins, and Kac-Moody Algebras
It has been known for a long time that the theory of electromagnetism in vacuum has the important property of electric-magnetic duality: one can exchange the role of electric and magnetic fields without changing the physics. Twenty years ago, this idea was generalized from electromagnetism to Einstein’s general relativity. The “magnetic” formulation of gravity is by now well understood at the linearised level, but a complete physical picture including interactions is still missing. The aim of this project is to establish and understand this duality in the non-linear and strong field regime. I will follow two lines of research. The first one will investigate a class of models in six dimensions containing chiral fields in place of a metric, which provide a new geometrical perspective on dual gravity upon dimensional reduction. The second one will explore higher dualities and their link with infinite-dimensional Lie algebras, with an emphasis on the three-dimensional higher-spin case.
31 years old