# Dimension formulae and generalised deep holes of the Leech lattice vertex operator algebra

```@article{Mller2019DimensionFA,
title={Dimension formulae and generalised deep holes of the Leech lattice vertex operator algebra},
author={Sven Karup M{\o}ller and Nils R. Scheithauer},
journal={Annals of Mathematics},
year={2019}
}```
• Published 11 October 2019
• Mathematics
• Annals of Mathematics
We prove a dimension formula for the weight-1 subspace of a vertex operator algebra \$V^{\operatorname{orb}(g)}\$ obtained by orbifolding a strongly rational, holomorphic vertex operator algebra \$V\$ of central charge 24 with a finite order automorphism \$g\$. Based on an upper bound derived from this formula we introduce the notion of a generalised deep hole in \$\operatorname{Aut}(V)\$. We then give a construction of all 70 strongly rational, holomorphic vertex operator algebras of central charge…

## Tables from this paper

• Mathematics
Journal of the London Mathematical Society
• 2022
We present a systematic, rigorous construction of all 70 strongly rational, holomorphic vertex operator algebras V\$V\$ of central charge 24 with non‐zero weight‐one space V1\$V_1\$ as cyclic orbifold
• Mathematics
• 2020
. We present a systematic, rigorous construction of all 70 strongly rational, holomorphic vertex operator algebras V of central charge 24 with non-zero weight-one space V 1 as cyclic orbifold
• Mathematics
Communications in Mathematical Physics
• 2023
We use the theory of topological modular forms to constrain bosonic holomorphic CFTs, which can be viewed as (0 , 1) SCFTs with trivial right-moving supersymmetric sector. A conjecture by Segal,
. We prove that all holomorphic vertex operator algebras of central charge 24 with non-trivial weight one subspaces are unitary. The main method is to use the orbifold construction of a holomorphic
• Mathematics
• 2022
. We prove that a haploid associative algebra in a C ∗ -tensor category C is equivalent to a Q-system (a special C ∗ -Frobenius algebra) in C if and only if it is rigid. This allows us to prove the
• Mathematics
• 2022
We classify all unitary, rational conformal field theories with two primaries, central charge c < 25, and arbitrary Wronskian index. We find that any such theory is either a Mathur–Mukhi–Sen (MMS)
• Mathematics
• 2022
We give a lattice theoretical interpretation of generalized deep holes of the Leech lattice VOA V Λ . We show that a generalized deep hole deﬁnes a “true” automorphism invariant deep hole of the
• Mathematics
Communications in Mathematical Physics
• 2022
. We describe the automorphism groups of all holomorphic vertex operator algebras of central charge 24 with non-trivial weight one Lie algebras by using their constructions as simple current
• Mathematics
• 2021
We associate with a generalised deep hole of the Leech lattice vertex operator algebra a generalised hole diagram. We show that this Dynkin diagram determines the generalised deep hole up to
• Mathematics
• 2021
We determine the automorphism groups of the cyclic orbifold vertex operator algebras associated with coinvariant lattices of isometries of the Leech lattice in the conjugacy classes 4C, 6E, 6G, 8E

## References

SHOWING 1-10 OF 93 REFERENCES

In this thesis we develop an orbifold theory for a finite, cyclic group G acting on a suitably regular, holomorphic vertex operator algebra V. To this end we describe the fusion algebra of the
. Modular invariant conformal field theories with just one primary field and central charge c = 24 are considered. It has been shown previously that if the chiral algebra of such a theory contains
We provide a novel and simple description of Schellekens’ seventy-one affine KacMoody structures of self-dual vertex operator algebras of central charge 24 by utilizing cyclic subgroups of the glue

### Reine Angew

• Math., 759:61–99,
• 2020
The theta function of a positive definite even lattice of even rank generates a representation of SL2(Z) on the group algebra of the discriminant form of the lattice. This representation goes back to
: We prove an orbifold conjecture for conformal ﬁeld theory with a solvable automorphism group. Namely, we show that if V is a C 2 -coﬁnite simple vertex operator algebra and G is a ﬁnite solvable
• Mathematics
• 2015
By applying Miyamoto’s Z3-orbifold construction to the lattice vertex operator algebras associated to Niemeier lattices and their automorphisms of order 3, we construct holomorphic vertex operator
• Mathematics
• 2021
We associate with a generalised deep hole of the Leech lattice vertex operator algebra a generalised hole diagram. We show that this Dynkin diagram determines the generalised deep hole up to