Exceptional Algebra and Sporadic Groups at c=12

Abstract

In earlier works, it was seen that a $\mathbb{Z}/2$ orbifold of the theory of 24 free two-dimensional chiral fermions admits various sporadic finite simple groups as global symmetry groups when viewed as an $\mathcal{N}=1$, $\mathcal{N}=2$, or $\mathcal{N}=4$ superconformal field theory. In this note, we show that viewing the same theory as an SCFT with extended $\mathcal{N}=1$ symmetry -- where the extension is the same one which arises in string compactification on manifolds of exceptional Spin$(7)$ holonomy -- yields theories which have global symmetry given by the sporadic groups $M_{24},C{o}_2$ or $C{o}_3$. The partition functions twined by these symmetries, when decomposed into characters of the Spin(7) algebra, give rise to two-component vector-valued mock modular forms encoding an infinite-dimensional module for the corresponding sporadic groups.

37 pages, including many tables

References in corpus (5)

• Mock Theta Functions
• Notes on the K3 Surface and the Mathieu group M_24
• Note on Twisted Elliptic Genus of K3 Surface
• Mock Modular Mathieu Moonshine Modules
• Generalised Mathieu Moonshine

Cited by in corpus (7)

• The 290 fixed-point sublattices of the Leech lattice
• Mock Modular Mathieu Moonshine Modules
• Self-Dual Vertex Operator Superalgebras and Superconformal Field Theory
• K3 String Theory, Lattices and Moonshine
• Sporadic and Exceptional
• Superconformal algebras for generalized Spin(7) and G${}_2$ connected sums
• On the elliptic genera of manifolds of Spin(7) holonomy