This seminar will be on Zoom (soon)!
Time: June 9, Fri 10:00 am - 12 noon ET Password: cmsa
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Gerald Höhn (Kansas State University) and Sven Möller (University of Hamburg).
Title: Classification of Self-Dual Vertex Operator Superalgebras of
Central Charge at Most 24
Abstract:
We discuss the classfication of self-dual vertex operator superalgebras
(SVOAs) of central charge 24, or in physics parlance the purely chiral
2-dimensional fermionic conformal field theories with just one primary
field.
There are exactly 969 such SVOAs under suitable regularity assumptions
and the assumption that the shorter moonshine module VB^# is the unique
self-dual SVOA of central charge 23.5 whose weight-1/2 and weight-1
spaces vanish.
We construct and classify the self-dual SVOAs by determining the
2-neighbourhood graph of the self-dual (purely bosonic) VOAs of central
charge 24 and also by realising them as simple-current extensions of a
dual pair containing a certain maximal lattice VOA. We show that all
SVOAs besides VB^# x F and potential fake copies thereof stem from
elements of the Conway group Co_0, the automorphism group of the Leech
lattice.
By splitting off free fermions F, if possible, we obtain the
classification for all central charges less than or equal to 24.
Reference: G. Höhn, S. Möller, arXiv:2303.17190.