Higher algebras in supergravity and M-theory

https://hu-berlin.zoom.us/j/61686623112

Maximal supergravity theories in 10 and 11 dimensions, which are the low-energy limits of string and M-theory,
exhibit rich and surprising mathematical features. Notably, upon dimensional reduction of d space-like dimensions they exhibit symmetries under the exceptional groups $E_{d(d)}$. These symmetries were completely mysterious from the viewpoint of the original theory. I introduce a framework called "exceptional field theory" that explains these symmetries. It is based on a novel kind of geometry, in which the diffeomorphism invariance underlying general relativity is unified with various "higher-form" symmetries. I elaborate on the higher algebraic structures that these generalized diffeomorphisms display, including Lie-infinity and Leibniz-Loday algebras.