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

2014/12/08 by Nathan Benjamin, Benjamin, Nathan, Sarah M. Harrison +7 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · pdf · doi:10.48550/arxiv.1412.2804

openalex publication_date 2014/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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 SW(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.

Citations

• K3 Surfaces, N=4 Dyons, and the Mathieu Group M24
• Three-Dimensional Gravity Revisited
• An algorithm for evaluating Gram matrices in Verma modules of W-algebras
• Exceptional Algebra and Sporadic Groups at c=12
• Vector-Valued Rademacher Sums and Automorphic Integrals
• Super-moonshine for Conway's largest sporadic group

Cited by

• Professor Nambu, String Theory and Moonshine Phenomenon

Related

• Exceptional Algebra and Sporadic Groups at c=12
• The Geometry of G₂, Spin(7), and Spin(8)-models
• The Geometry and Superconformal Algebras of String Compactifications with a G-structure
• M-theory on manifolds of G2 holonomy: the first twenty years
• Relation Between Holonomy Groups in Superstrings, M and F-theories