Conformal field theories with sporadic group symmetry

DOI10.1007/s00220-021-04207-7zbMath1503.81056arXiv2002.02970OpenAlexW3205685196MaRDI QIDQ2244083

Jeffrey A. Harvey, Brandon C. Rayhaun, Sungjay Lee, Jin-Beom Bae, Ki-Myeong Lee

Publication date: 11 November 2021

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.02970

Mathematics Subject Classification ID

Simple groups: sporadic groups (20D08) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Vertex operators; vertex operator algebras and related structures (17B69) Operator algebra methods applied to problems in quantum theory (81R15) Hecke-Petersson operators, differential operators (several variables) (11F60)

Related Items

BPS algebras in 2D string theory, On classification of fermionic rational conformal field theories, Hecke relations among 2d fermionic RCFTs, Hecke relations, cosets and the classification of 2d RCFTs, Classification of unitary RCFTs with two primaries and central charge less than 25, Duality defects in \(E_8\), Holomorphic modular bootstrap revisited, Bootstrapping fermionic rational CFTs with three characters

Uses Software

• GAP
• Magma
• SageMath

Cites Work

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• Umbral moonshine and the Niemeier lattices
• Proof of the umbral moonshine conjecture
• Traces of singular moduli and moonshine for the Thompson group
• Much ado about Mathieu
• Modular differential equations and null vectors
• Rademacher sums, moonshine and gravity
• Umbral moonshine
• A proof of the Thompson moonshine conjecture
• Operator content of two-dimensional conformally invariant theories
• The group of symmetries of the shorter Moonshine module
• \(EE_8\)-lattices and dihedral groups
• Exact half-BPS black hole entropies in CHL models from Rademacher series
• Conformal field theory
• A conformal block Farey tail
• \(K3\) surfaces, \({\mathcal N}=4\) dyons and the Mathieu group \(M_{24}\)
• McKay's \(E_6\) observation on the largest Fischer group
• Modularity in orbifold theory for vertex operator superalgebras
• Fusion rules and modular transformations in 2D conformal field theory
• Fusion rules for the vertex operator algebras \(M(1)^+\) and \(V_L^+\)
• The 290 fixed-point sublattices of the Leech lattice
• Classical and quantum conformal field theory
• A modern fareytail
• Super-moonshine for Conway's largest sporadic group
• A simple construction for the Fischer-Griess monster group
• Unitary representations of the Virasoro and super-Virasoro algebras
• Beauty and the beast: Superconformal symmetry in a monster module
• Virasoro algebras and coset space models
• The operator algebra of orbifold models
• The friendly giant
• Vertex operator algebras associated to representations of affine and Virasoro algebras
• A conjugacy theorem for \(E_8\)
• Framed vertex operator algebras, codes and the moonshine module
• The maximal subgroups of the Baby Monster. I
• Representations of vertex operator algebra \(V_L^+\) for rank one lattice \(L\)
• Nonabelian orbifolds and the boson-fermion correspondence
• The Magma algebra system. I: The user language
• Vertex operator algebra with two Miyamoto involutions generating \(S_{3}\).
• Vertex operator algebras generated by two conformal vectors whose \(\tau\)-involutions generate \(S_{3}\).
• Classification of irreducible modules for the vertex operator algebra \(V_{L}^{+}\): general case.
• Decompositions of the moonshine module with respect to subVOAs associated to codes over \(\mathbb Z_{2k}\)
• Two-dimensional RCFT's without Kac-Moody symmetry
• 2A-orbifold construction and the baby-monster vertex operator superalgebra
• Vertex operator algebras, Higgs branches, and modular differential equations
• Hecke relations in rational conformal field theory
• Associative subalgebras of the Griess algebra
• Monstrous moonshine and monstrous Lie superalgebras
• The kernel of the modular representation and the Galois action in RCFT
• Griess algebras and conformal vectors in vertex operator algebras
• Conformal field theories, representations and lattice constructions
• Twisted elliptic genus for \(K3\) and Borcherds product
• \(\mathbb{Z}_2 \times \mathbb{Z}_2\) codes and vertex operator algebras
• \(6A\)-algebra and its representations
• Supersymmetry and the Suzuki chain
• Properties of extremal CFTs with small central charge
• Uniqueness of VOA structure of \(3C\)-algebra and \(5A\)-algebra
• Mathieu moonshine in the elliptic genus of K3
• Schur-Weyl duality for Heisenberg cosets
• Monster anatomy
• On Rademacher sums, the largest Mathieu group and the holographic modularity of moonshine
• Quasi-lisse vertex algebras and modular linear differential equations
• The character table of \(2_+^{1+22}.Co_2\).
• Hypergeometric series, modular linear differential equations and vector-valued modular forms
• Rademacher expansions and the spectrum of 2d CFT
• Integrable and conformal boundary conditions for ℤ_kparafermions on a cylinder
• THE MOONSHINE MODULE FOR CONWAY’S GROUP
• Rademacher Sums and Rademacher Series
• Mirror extensions of rational vertex operator algebras
• McKay’s E7 Observation on the Baby Monster
• A natural representation of the Fischer-Griess Monster with the modular function J as character
• The Maximal Subgroups of the Fischer Groups Fi ₂₄ and Fi′ ₂₄
• Remarks on Classical Invariant Theory
• Monstrous Moonshine
• Construction of Automorphic Forms and Integrals
• A Simple Subgroup of M ? and E ₈ (3)
• Modular invariance of characters of vertex operator algebras
• Notes on the K3 Surface and the Mathieu GroupM₂₄
• Research topics in finite groups and vertex algebras
• 6-Transposition Property of  -Involutions of Vertex Operator Algebras
• Modular-invariance of trace functions in orbifold theory and generalized Moonshine.
• Fusion rules for the charge conjugation orbifold