Conformal Designs based on Vertex Operator Algebras

Abstract

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 fixed degree of an extremal self-dual vertex operator algebra form conformal 11-, 7-, or 3-designs, generalizing similar results of Assmus-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.

35 pages with 1 table, LaTeX

References in corpus (4)

• Modular invariance of trace functions in orbifold theory
• Framed vertex operator algebras, codes and the moonshine module
• Norton's Trace Formulae for the Griess Algebra of a Vertex Operator Algebra with Larger Symmetry
• The space of graded traces for holomorphic VOAs of small central charge

Cited by in corpus (7)

• Three-Dimensional Gravity Revisited
• Bounds on Operator Dimensions in 2D Conformal Field Theories
• Bounds for State Degeneracies in 2D Conformal Field Theory
• Fermionic CFTs from classical codes over finite fields
• Non-chiral 2d CFT with integer energy levels
• Self-Dual Vertex Operator Superalgebras of Large Minimal Weight
• Universal Bounds in Even-Spin CFTs