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Lie Group Quantum Mathematics Seminar

Borcherds-Kac-Moody superalgebras and superstrings

Roberto Volpato, University of Padova

Location:  Zoom
Date & time: Friday, 24 March 2023 at 12:10PM - 1:10PM

Abstract There are several known examples of Borcherds-Kac-Moody (BKM) (super)algebras that can be constructed as the space of
physical states in a suitable vertex (super)algebra (VA) (a chiral superstring, in physics parlance). Famously, one of these examples was a key ingredient in the proof of the Monstrous moonshine conjecture. We discuss a particular case of this construction, which leads to a BKM superalgebra with a natural action of the Conway group Co0, induced by an action on the corresponding VA by vertex algebra automorphisms. On more general grounds, we describe how some of the BKM algebras constructed in this way can arise in low dimensional compactification of a (non-chiral) superstring theory. This perspective sheds a new light on the relation between BKM algebras and Moonshine conjectures. No prior knowledge of string theory is assumed.

Zoom link
Meeting ID: 939 2146 5287
Passcode: 196884, the dimension of the weight 2 homogeneous
subspace of the moonshine module

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