Conformal Field Theories with Sporadic Group Symmetry

Abstract

The monster sporadic group is the automorphism group of a central charge $c=24$ vertex operator algebra (VOA) or meromorphic conformal field theory (CFT). In addition to its $c=24$ stress tensor $T(z)$, this theory contains many other conformal vectors of smaller central charge; for example, it admits $48$ commuting $c=\frac{1}{2}$ conformal vectors whose sum is $T(z)$. Such decompositions of the stress tensor allow one to construct new CFTs from the monster CFT in a manner analogous to the Goddard-Kent-Olive (GKO) coset method for affine Lie algebras. We use this procedure to produce evidence for the existence of a number of CFTs with sporadic symmetry groups and employ a variety of techniques, including Hecke operators, modular linear differential equations, and Rademacher sums, to compute the characters of these CFTs. Our examples include (extensions of) nine of the sporadic groups appearing as subquotients of the monster, as well as the simple groups ${}^2{E}_6(2)$ and $F_4(2)$ of Lie type. Many of these examples are naturally associated to McKay's $\widehat{E_8}$ correspondence, and we use the structure of Norton's monstralizer pairs more generally to organize our presentation.

arXiv comment109 pages, 5 figures, new results for D4B case added as well as new material on the use of Rademacher sums to determine characters of the dual CFTs

References in corpus (31)

• Vertex Algebras and Algebraic Curves
• Modular invariance of trace functions in orbifold theory
• Applied Conformal Field Theory
• Notes on the K3 Surface and the Mathieu group M_24
• A Black Hole Farey Tail
• Vertex operator algebras, Higgs branches, and modular differential equations
• Framed vertex operator algebras, codes and the moonshine module
• A Farey Tail for Attractor Black Holes
• Note on Twisted Elliptic Genus of K3 Surface
• The kernel of the modular representation and the Galois action in RCFT
• Conformal Field Theories, Representations and Lattice Constructions
• Schur-Weyl Duality for Heisenberg Cosets
• Modular differential equations and null vectors
• Mathieu Moonshine in the elliptic genus of K3
• Representations of vertex operator algebra V_L^+ for rank one lattice L
• A conformal block Farey tail
• Rademacher Expansions and the Spectrum of 2d CFT
• Hecke Relations in Rational Conformal Field Theory
• Modularity in orbifold theory for vertex operator superalgebras
• Two-dimensional RCFT's without Kac-Moody symmetry
• Selbstduale Vertexoperatorsuperalgebren und das Babymonster (Self-dual Vertex Operator Super Algebras and the Baby Monster)
• The 290 fixed-point sublattices of the Leech lattice
• Classification of RCFT from Holomorphic Modular Bootstrap: A Status Report
• A proof of the Thompson Moonshine Conjecture
• Traces of Singular Moduli and Moonshine for the Thompson Group
• Pariah moonshine
• Vector-Valued Rademacher Sums and Automorphic Integrals
• Monster Anatomy
• Integrable and Conformal Boundary Conditions for Z_k Parafermions on a Cylinder
• Duality Defect of the Monster CFT
• Exact Half-BPS Black Hole Entropies in CHL Models from Rademacher Series

Cited by in corpus (11)

• Duality Defects in $E_8$
• Holomorphic modular bootstrap revisited
• Bootstrapping Fermionic Rational CFTs with Three Characters
• Galois Symmetry Induced by Hecke Relations in Rational Conformal Field Theory and Associated Modular Tensor Categories
• Classification of Unitary RCFTs with Two Primaries and Central Charge Less Than 25
• Hecke Relations, Cosets and the Classification of 2d RCFTs
• On Classification of Fermionic Rational Conformal Field Theories
• Self-dual $S_3$-invariant quantum chains
• BPS Algebras in 2D String Theory
• Fermionic Rational Conformal Field Theories and Modular Linear Differential Equations
• Monstrous M-theory