Self-Dual Vertex Operator Superalgebras of Large Minimal Weight

Understand

The new general upper bound mu <= [c/24] + 1 for the minimal weight mu of a self-dual vertex operator superalgebra of central charge c different from 47/2 is proven.

• For central charges c <= 48, further improved estimates are given and examples of with large minimal weight are discussed.
• We also study the case of vertex operator superalgebras with N=1 supersymmetry which was first considered by Witten in connection with three-dimensional quantum gravity.
• The upper bound mu^* <= (1/2)[c/12]+1/2 for the minimal superconformal weight is obtained for c different from 47/2.