# Most Vertex Superalgebras Associated to an Odd Unimodular Lattice of Rank 24 Have an Superconformal Structure

@article{Hohn2021MostVS, title={Most Vertex Superalgebras Associated to an Odd Unimodular Lattice of Rank 24 Have an Superconformal Structure}, author={Gerald Hohn and Geoffrey Mason}, journal={Experimental Mathematics}, year={2021} }

Odd, positive-definite, integral, unimodular lattices N of rank 24 were classified by Borcherds. There are 273 isometry classes of such lattices. Associated to them are vertex superalgebras $V_N$ of central charge c=24. We show that at least 267 of these vertex operator superalgebras contain an N=4 superconformal subalgebra of central charge $c'=6$. This is achieved by studying embeddings $L+\subseteq N$ of a certain rank 6 lattice L+.

## Tables from this paper

## One Citation

Decompositions of index one Jacobi forms into $N=4$ characters and formulas for mock modular forms

- Mathematics
- 2021

It is shown that every weak Jacobi form of weight zero and index one on a congruence subgroup of the full Jacobi group can be decomposed into N = 4 superconformal characters. Additionally, a simple…

## References

SHOWING 1-10 OF 17 REFERENCES

$N=2$ and $N=4$ Subalgebras of Super Vertex Operator Algebras

- Mathematics
- 2016

We develop criteria to decide if an $N=2$ or $N=4$ super conformal algebra is a subalgebra of a super vertex operator algebra in general, and of a super lattice theory in particular. We give some…

Generalized vertex algebras and relative vertex operators

- Mathematics
- 1993

1. Introduction. 2. The setting. 3. Relative untwisted vertex operators. 4. Quotient vertex operators. 5. A Jacobi identity for relative untwisted vertex operators. 6. Generalized vertex operator…

Notes on the K3 Surface and the Mathieu Group M 24

- Mathematics, Computer ScienceExp. Math.
- 2011

We point out that the elliptic genus of the K3 surface has a natural decomposition in terms of dimensions of irreducible representations of the largest Mathieu group M 24. The reason remains a…

Sphere packings, I

- Mathematics, Computer ScienceDiscret. Comput. Geom.
- 1997

A program to prove the Kepler conjecture on sphere packings is described and it is shown that every Delaunay star that satisfies a certain regularity condition satisfies the conjecture.

The Leech lattice and other lattices

- Mathematics
- 1999

This is an unpublished manuscript written in 1983-4. It contains several results about lattices (=integral quadratic forms) including the classification of the unimodular lattices in dimensions up to…

Vertex algebras for beginners

- Mathematics
- 1997

Preface. 1: Wightman axioms and vertex algebras. 1.1: Wightman axioms of a QFT. 1.2: d = 2 QFT and chiral algebras. 1.3: Definition of a vertex algebra. 1.4: Holomorphic vertex algebras. 2: Calculus…

Introduction to Vertex Operator Algebras and Their Representations

- Mathematics
- 2003

1 Introduction.- 1.1 Motivation.- 1.2 Example of a vertex operator.- 1.3 The notion of vertex operator algebra.- 1.4 Simplification of the definition.- 1.5 Representations and modules.- 1.6…

The Magma Algebra System I: The User Language

- Computer Science, MathematicsJ. Symb. Comput.
- 1997

The MAGMA language is presented, the design principles and theoretical background are outlined, and the constructors for structures, maps, and sets are outlined.

"J."

- 1890

however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)…

- J. Phys. A: Math. Theoret.
- 2017