Conformal designs based on vertex operator algebras
By Gerald Hoehn. 2007
64 citations recorded by the source corpus.
We introduce the notion of a conformal design based on a vertex operator algebra. This notation is a natural analog of the notion of block designs or spherical designs when the elements of the design are based on self-orthogonal binary codes or integral lattices, respectively. It is shown that the subspaces of an extremal self-dual vertex operator algebra of fixed degree form conformal 11-, 7-, or 3-designs, generalizing similar results of Assmus and Mattson and Venkov for extremal doubly-even codes and extremal even lattices. Other examples are coming from group actions on vertex operator algebras, the case studied first by Matsuo. The classification of conformal 6- and 8-designs is investigated. Again, our results are analogous to similar results for codes and lattices.
Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/fa2c5741d3e7677e78871c9e8a85e3d2a5ba56d9
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In Artificial Intelligence
In Discrete Mathematics and Combinatorics
In Numerical Analysis
Citations in the corpus
- Three-Dimensional Gravity Revisited (2007, background): “Conformal field theories with this property were first investigated by Höhn in [31,32] and have been called extremal CFT’s; see also [33].”
- A universal inequality for CFT and quantum gravity (2009, unknown): “Such a conclusion would fit well with the results [9, 10, 6, 25].”