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Higher Algebras in Supergravity and M-theory

Posted in
Olaf Hohm
HU Berlin
Tue, 14/12/2021 - 13:45 - 15:30


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.

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