On the elliptic genera of manifolds of Spin(7) holonomy

Abstract

Superstring compactification on a manifold of Spin(7) holonomy gives rise to a 2d worldsheet conformal field theory with an extended supersymmetry algebra. The $\mathcal{N}=1$ superconformal algebra is extended by additional generators of spins 2 and 5/2, and instead of just superconformal symmetry one has a $c=12$ realization of the symmetry group $\mathcal{S}\mathcal{W}(3/2,2)$. In this paper, we compute the characters of this supergroup, and decompose the elliptic genus of a general Spin(7) compactification in terms of these characters. We find suggestive relations to various sporadic groups, which are made more precise in a companion paper.

46 pages, 6 figures. v2: minor typos corrected in sec. 3

References in corpus (8)

• Three-Dimensional Gravity Revisited
• Mock Theta Functions
• Notes on the K3 Surface and the Mathieu group M_24
• Note on Twisted Elliptic Genus of K3 Surface
• K3 Surfaces, N=4 Dyons, and the Mathieu Group M24
• Exceptional Algebra and Sporadic Groups at c=12
• Comments on M${}_{24}$ representations and $C{Y}_3$ geometries
• Super-moonshine for Conway's largest sporadic group

Cited by in corpus (1)

• Professor Nambu, String Theory and Moonshine Phenomenon