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

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arxiv 1412.2804 v2 pith:NV6IANTL submitted 2014-12-08 hep-th

Nathan Benjamin , Sarah M. Harrison , Shamit Kachru , Natalie M. Paquette , Daniel Whalen This is my paper · ORCID
classification hep-th
keywords spinalgebracharacterscompactificationellipticextendedholonomymathcal
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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 $\mathcal{SW}(3/2,2)$. 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.

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  1. $\mathcal{SW}$-algebras and strings with torsion

    hep-th 2024-12 conditional novelty 6.0 of 10

    For G2 and SU(3) string backgrounds with NS flux, the scalar torsion class controls the first-order deformation of the worldsheet super W-algebra couplings away from special holonomy.

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