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.

109 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

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Cited by in corpus (9)

• Duality Defects in $E_8$
• Holomorphic modular bootstrap revisited
• Bootstrapping Fermionic Rational CFTs with Three Characters
• 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
• BPS Algebras in 2D String Theory
• Fermionic Rational Conformal Field Theories and Modular Linear Differential Equations
• Monstrous M-theory