Seminar for Algebra, SCE QuantiXLie

On Friday, October 27, 2023, two lectures will be held as part of Seminar for Algebra in lecture room A001, Department of Mathematics.

15:00 hours

Hannes Knötzele (University of Hamburg)

On Cyclic Orbifolds of Rational Vertex Operator Algebras

Abstract:
For a holomorphic vertex operator algebra (VOA) V with a finite cyclic group G of automorphisms, the category of modules of the fixed point vertex operator subalgebra V^G is equivalent to the module category of a twisted Drinfeld double of G. For a rational but not necessarily holomorphic VOA V, a general description of the category of modules of V^G is unknown. In this talk, I will sketch the main difficulties facing this problem. First, I will recall categorical prerequisites like equivariantisation and crossed modular categories. Then, I will apply these ideas to examples that generalise Tambara-Yamagami categories.

16:00 hours

Sven Möller (University of Hamburg)

Classification of Self-Dual Vertex Operator Superalgebras of Central Charge 24

Abstract:
We classify the self-dual (or holomorphic) vertex operator superalgebras (SVOAs) of central charge 24, or in physics parlance the purely
left-moving, spin 2-dimensional 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. Additionally, there might be self-dual SVOAs arising as "fake copies" of VB^# tensored with a free fermion F. 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. This is based on joint work with Gerald Höhn.

All Seminar members and others interested are invited.