Modularity of Relatively Rational Vertex Algebras and Fusion Rules of Principal Affine W-Algebras

Abstract

We study modularity of the characters of a vertex (super)algebra equipped with a family of conformal structures. Along the way we introduce the notions of rationality and cofiniteness relative to such a family. We apply the results to determine modular transformations of trace functions on admissible modules over affine Kac-Moody algebras and, via BRST reduction, trace functions on minimal series representations of principal affine W-algebras.

33 pages, LaTeX; slight change to title, expanded proof of Theorem 5.13, other minor corrections; to appear in Comm. Math. Phys

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