Constraints on extremal self-dual CFTs
High Energy Physics - Theory
2008-11-26 v2
Abstract
We argue that the existence of a modular differential equation implies that a certain vector vanishes in Zhu's C2 quotient space, and we check this assertion in numerous examples. If this connection is true in general, it would imply that the recently conjectured extremal self-dual conformal field theories at c=24 k cannot exist for k\geq 42.
Keywords
Cite
@article{arxiv.0707.4073,
title = {Constraints on extremal self-dual CFTs},
author = {Matthias R. Gaberdiel},
journal= {arXiv preprint arXiv:0707.4073},
year = {2008}
}
Comments
16 pages LaTeX; v1: rewritten to make paper more self-contained, modified conjecture slightly (this has no effect on main conclusion), added references