The space of graded traces for holomorphic VOAs of small central charge

Details The space of graded traces for holomorphic VOAs of small central charge The space of graded traces for holomorphic VOAs of small central charge

2006-06-12

arxiv.org/abs/math/0606282v1

Mathematics

Quantum Algebra

34 pages; See also http://www.math.gatech.edu/~hurley

Scientific paper

It is one of the remarkable results of vertex operator algebras (VOAs) that the graded traces (one-point correlation functions) of holomorphic VOAs are modular functions. This paper explores the question of which modular functions arise as the graded traces of holomorphic VOAs. For VOAs of small central charge, i.e., $c\le 24$, and a non-zero weight-one subspace, we find that the only conditions imposed on the modular fuctions are those that arise easily out of our condition that the VOAs be of CFT type, that is that they have no negative-weight subspaces and their zero-weight subspace is generated by the vacuum vector.

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