CMSA Quantum Matter in Mathematics and Physics: Classification of Self-Dual Vertex Operator Superalgebras of Central Charge at Most 24
SEMINARS, CMSA EVENTS
Speaker:
Gerald Höhn, Kansas State University and Sven Möller, University of Hamburg
We discuss the classification 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.
https://cmsa.fas.harvard.edu/
--------
Subscribe to Harvard CMSA Quantum Matter and other seminar videos
(more to be uploaded):
https://www.youtube.com/
Subscribe to Harvard CMSA seminar mailing list:
https://forms.gle/