On $${\mathbb {Z}}_p$$ Z p -orbifold constructions of the Moonshine vertex operator algebra

Abe, Tokiharu; Lam, Ching Hung; Yamada, Hiromichi

doi:10.1007/s00209-017-2036-3

Cited by 4 publications

(8 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof. Since the statement is verified in the sense of vertex algebras in [ALY17], it suffices to transfer the claim to the conformal net setting. The work on "framed CFTs" from [Bis12, Chapter 7] verifies analytically the isomorphism (V Λ ) Z 2 ∼ = V ♮ .…”

Section: Proof Of Theoremmentioning

confidence: 97%

“…In the Leech case, Aut(V Λ ) is in fact equal to Λ.O(Λ) by [DN99, Theorem 2.1] and the fact the Leech lattice Λ has no roots (so that the connected Lie group group called "N " in [DN99] is just Λ). In the sense of vertex algebras, the following result is definitional for p = 2, conjectured in [FLM88,Tui92] for p ∈ {3, 5, 7, 13}, announced for p = 3 in [DM94], and proved in full in [ALY17]:…”

Section: Proof Of Theoremmentioning

confidence: 99%

See 1 more Smart Citation

The Moonshine Anomaly

Johnson-Freyd

2019

Commun. Math. Phys.

View full text Add to dashboard Cite

The anomaly for the Monster group M acting on its natural (aka moonshine) representation V ♮ is a particular cohomology class ω ♮ ∈ H 3 (M, U(1)) that arises as a conformal field theoretic generalization of the second Chern class of a representation. This paper shows that ω ♮ has order exactly 24 and is not a Chern class. In order to perform this computation, this paper introduces a finite-group version of T-duality, which is used to relate ω ♮ to the anomaly for the Leech lattice CFT.

show abstract

Section: Proof Of Theoremmentioning

confidence: 97%

Section: Proof Of Theoremmentioning

confidence: 99%

The Moonshine Anomaly

Johnson-Freyd

2019

Commun. Math. Phys.

View full text Add to dashboard Cite

show abstract

“…In [1], several constructions of V were given by cyclic orbifolds of odd prime order p on V Λ , and analyzed using cyclic orbifolds of order 2p in order to produce a comparison with the original order 2 orbifold construction of [27]. We will apply a similar method to produce actions of the monster on orbifolds over various rings.…”

Section: The Abe-lam-yamada Methodsmentioning

confidence: 99%

“…I would like to thank Toshiyuki Abe for describing the constructions in [1] in detail at the "VOA and related topics" workshop at Osaka University in March 2017. I would also like to thank the anonymous referees for many helpful comments, and one referee in particular for their help with the proof of Lemma 2.13.…”

Section: Acknowledgementsmentioning

confidence: 99%

A Self-Dual Integral Form of the Moonshine Module

Carnahan

2019

SIGMA

View full text Add to dashboard Cite

We construct a self-dual integral form of the moonshine vertex operator algebra, and show that it has symmetries given by the Fischer-Griess monster simple group. The existence of this form resolves the last remaining open assumption in the proof of the modular moonshine conjecture by Borcherds and Ryba. As a corollary, we find that Griess's original 196884-dimensional representation of the monster admits a positive-definite self-dual integral form with monster symmetry.In this paper, we construct self-dual R-forms of the moonshine module vertex operator algebra [27] over various commutative rings R, culminating in the universal case where R is the ring of rational integers Z. For the Z-form, we show that the vertex operator algebra has monster symmetry, and is self-dual with respect to an invariant bilinear form that respects the monster symmetry. Base change then gives us self-dual monster-symmetric vertex operator algebras over any commutative ring. Our construction yields the final step in the affirmative resolution of Ryba's modular moonshine conjecture.This paper is a contribution to the Special Issue on Moonshine and String Theory. The full collection is available at https://www.emis.de/journals/SIGMA/moonshine.html arXiv:1710.00737v4 [math.RT] 19 Apr 2019Given a homomorphism f : R → S of commutative rings, we say f is faithfully flat if S is faithfully flat as an R-module under the induced action.See [43, Section 00H9] for a brief overview of basic properties of flat and faithfully flat modules and ring maps.Definition 2.2. Let f : R → S be a homomorphism of commutative rings. A descent datum for modules with respect to f is a pair (M, φ), where M is an S-module, and φ : M ⊗ R S → S ⊗ R M is an S ⊗ R S-module isomorphism satisfying the "cocycle condition", i.e., that the following diagram commutes:

show abstract

“…• Our investigation of Z 2A has a natural generalization to Z pA with p a prime number dividing the order of the Monster group. For each such p, the Monster CFT is known to be self-dual under the Z pA orbifold [46,29,30,48,49]. 18 , which implies that the Monster CFT must have a duality defect belonging to a Z p Tamabara-Yamagami category.…”

Section: Open Questionsmentioning

confidence: 99%

Duality defect of the monster CFT

Lin¹,

Shao²

2021

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We show that the fermionization of the Monster CFT with respect to Z 2 A is the tensor product of a free fermion and the Baby Monster CFT. The chiral fermion parity of the free fermion implies that the Monster CFT is self-dual under the Z 2 A orbifold, i.e. it enjoys the Kramers–Wannier duality. The Kramers–Wannier duality defect extends the Monster group to a larger category of topological defect lines that contains an Ising subcategory. We introduce the defect McKay–Thompson series defined as the Monster partition function twisted by the duality defect, and find that the coefficients can be decomposed into the dimensions of the (projective) irreducible representations of the Baby Monster group. We further prove that the defect McKay–Thompson series is invariant under the genus-zero congruence subgroup 16D 0 of P S L ( 2 , Z ) .

show abstract

On $${\mathbb {Z}}_p$$ Z p -orbifold constructions of the Moonshine vertex operator algebra

Cited by 4 publications

References 35 publications

The Moonshine Anomaly

The Moonshine Anomaly

A Self-Dual Integral Form of the Moonshine Module

Duality defect of the monster CFT

Contact Info

Product

Resources

About