On orbifold constructions associated with the Leech lattice vertex operator algebra

@article{Lam2018OnOC,
  title={On orbifold constructions associated with the Leech lattice vertex operator algebra},
  author={Ching Hung Lam and Hiroki Shimakura},
  journal={Mathematical Proceedings of the Cambridge Philosophical Society},
  year={2018},
  volume={168},
  pages={261 - 285}
}
  • C. Lam, Hiroki Shimakura
  • Published 3 May 2017
  • Mathematics
  • Mathematical Proceedings of the Cambridge Philosophical Society
Abstract In this paper, we study orbifold constructions associated with the Leech lattice vertex operator algebra. As an application, we prove that the structure of a strongly regular holomorphic vertex operator algebra of central charge 24 is uniquely determined by its weight one Lie algebra if the Lie algebra has the type A3,43A1,2, A4,52, D4,12A2,6, A6,7, A7,4A1,13, D5,8A1,2 or D6,5A1,12 by using the reverse orbifold construction. Our result also provides alternative constructions of these… 
View on Cambridge Press
arxiv.org
20 Citations
Highly Influential Citations
1
Background Citations
6
Methods Citations
1

20 Citations

Extra automorphisms of cyclic orbifolds of lattice vertex operator algebras
In this article, we study the automorphism group of the cyclic orbifold of a vertex operator algebra associated with a rootless even lattice for a lift of a fixed-point free isometry of odd prime…
Automorphism groups of cyclic orbifold vertex operator algebras associated with the Leech lattice and some non-prime isometries
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…
Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices
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 V1 as cyclic orbifold…
A Geometric Classification of the Holomorphic Vertex Operator Algebras of Central Charge 24
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…
Q A ] 1 5 M ar 2 02 1 EXTRA AUTOMORPHISMS OF CYCLIC ORBIFOLDS OF LATTICE VERTEX OPERATOR ALGEBRAS
In this article, we study the automorphism group of the cyclic orbifold of a vertex operator algebra associated with a rootless even lattice for a lift of a fixed-point free isometry of odd prime…
INERTIA GROUPS AND UNIQUENESS OF HOLOMORPHIC VERTEX OPERATOR ALGEBRAS
We continue our program on classiffication of holomorphic vertex operator algebras of central charge 24. In this article, we show that there exists a unique strongly regular holomorphic VOA of…
Systematic orbifold constructions of Schellekens' vertex operator algebras from Niemeier lattices
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…
Dimension Formulae and Generalised Deep Holes of the Leech Lattice Vertex Operator Algebra
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…
Automorphism groups and uniqueness of holomorphic vertex operator algebras of central charge $24$
. 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…
A lattice theoretical interpretation of generalized deep holes of the Leech lattice vertex operator algebra
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…
...
...

References

SHOWING 1-10 OF 50 REFERENCES
A Cyclic Orbifold Theory for Holomorphic Vertex Operator Algebras and Applications
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…
A Cyclic Orbifold Theory for Holomorphic Vertex Operator Algebras and Applications
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…
A ℤ3-Orbifold Theory of Lattice Vertex Operator Algebra and ℤ3-Orbifold Constructions
For an even positive definite lattice L and its automorphism σ of order 3, we prove that a fixed point subVOA \(V_{L}^{\sigma}\) of a lattice VOA V L is C 2-cofinite. Using this result and the…
Holomorphic vertex operator algebras of small central charge
We provide a rigorous mathematical foundation to the study of strongly rational, holomorphic vertex operator algebras V of central charge c = 8, 16 and 24 initiated by Schellekens. If c = 8 or 16 we…
Construction and classification of holomorphic vertex operator algebras
Abstract We develop an orbifold theory for finite, cyclic groups acting on holomorphic vertex operator algebras. Then we show that Schellekens’ classification of V1{V_{1}}-structures of meromorphic…
The algebraic structure of relative twisted vertex operators
Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24
In 1993, Schellekens [‘Meromorphic c=24 conformal field theories’, Comm. Math. Phys. 153 (1993) 159–185.] obtained a list of possible 71 Lie algebras of holomorphic vertex operator algebras with…
Orbifold Construction of Holomorphic Vertex Operator Algebras Associated to Inner Automorphisms
In this article, we construct three new holomorphic vertex operator algebras of central charge 24 using the $${\mathbb{Z}_{2}}$$Z2-orbifold construction associated to inner automorphisms. Their…
Modular-Invariance of Trace Functions¶in Orbifold Theory and Generalized Moonshine
Abstract: The goal of the present paper is to provide a mathematically rigorous foundation to certain aspects of the theory of rational orbifold models in conformal field theory, in other words the…
Rational vertex operator algebras and the effective central charge
We establish that the Lie algebra of weight 1 states in a (strongly) rational vertex operator algebra is reductive, and that its Lie rank 1 is bounded above by the effective central charge c~. We…
...
...