arXiv subjects

Sarah M. Harrison

Publications and source records attributed to Sarah M. Harrison.

22 records · Page 2Linked to original sources

arXiv2016

Extremal chiral $\mathcal N=4$ SCFT with $c=24$

We construct an extremal chiral $\mathcal N=4$ superconformal field theory with central charge 24 from a $\mathbb Z_2$ orbifold of the chiral bosonic theory with target $\mathbb R^{24}/Λ$, where $Λ$ is the Niemeier lattice with root system $A_2^{12}$. This construction is analogous to constructions of extremal chiral $\mathcal N=1$ and $\mathcal N=2$ CFTs with $c=24$, where $Λ= Λ_{Leech}$ and the Niemeier lattice with root system $A_1^{24}$, respectively. The theory has a discrete symmetry group related to the sporadic group $M_{11}$.

hep-th↗

arXiv2015

Equivariant K3 Invariants

In this note, we describe a connection between the enumerative geometry of curves in K3 surfaces and the chiral ring of an auxiliary superconformal field theory. We consider the invariants calculated by Yau--Zaslow (capturing the Euler characters of the moduli spaces of D2-branes on curves of given genus), together with their refinements to carry additional quantum numbers by Katz--Klemm--Vafa (KKV), and Katz--Klemm--Pandharipande (KKP). We show that these invariants can be reproduced by studying the Ramond ground states of an auxiliary chiral superconformal field theory which has recently been observed to give rise to mock modular moonshine for a variety of sporadic simple groups that are subgroups of Conway's group. We also study equivariant versions of these invariants. A K3 sigma model is specified by a choice of 4-plane in the K3 D-brane charge lattice. Symmetries of K3 sigma models are naturally identified with 4-plane preserving subgroups of the Conway group, according to the work of Gaberdiel--Hohenegger--Volpato, and one may consider corresponding equivariant refined K3 Gopakumar--Vafa invariants. The same symmetries naturally arise in the auxiliary CFT state space, affording a suggestive alternative view of the same computation. We comment on a lift of this story to the generating function of elliptic genera of symmetric products of K3 surfaces.

hep-th↗

arXiv2015

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

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.

hep-th↗

arXiv2015

Exceptional Algebra and Sporadic Groups at c=12

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 ${\cal N}=1$, ${\cal N}=2$, or ${\cal N}=4$ superconformal field theory. In this note, we show that viewing the same theory as an SCFT with extended ${\cal N}=1$ 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 $M_{24}, Co_2$ or $Co_3$. 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.

hep-th↗