Curiosities above c = 24

Abstract

Two-dimensional rational CFT are characterised by an integer ℓ, related to the number of zeroes of the Wronskian of the characters. For two-character RCFT's with ℓ < 6 there is a finite number of theories and most of these are classified. Recently it has been shown that for ℓ ≥ 6 there are infinitely many admissible characters that could potentially describe CFT's. In this note we examine the ℓ = 6 case, whose central charges lie between 24 and 32, and propose a classification method based on cosets of meromorphic CFT's. We illustrate the method using theories on Kervaire lattices with complete root systems. In the process we construct the first known two-character RCFT's beyond ℓ = 2.

Discreteness and integrality in Conformal Field Theory

“…What this means is that it contains a lower-dimensional subrepresentation, whose complement is not itself a representation. 22 Indeed, by inspecting the S-matrix, 35) and by diagonality of the T -matrix, we see that {χ 0 + χ 4 , χ 2 } decouple from {χ 1 , χ 3 } and form their own two-dimensional subrepresentation R 2 . It is easy to check that m…”

“…The study of vvmfs has a long history in both physics (e.g. [27][28][29][30][31][32][33][34][35][36][37][38]) and mathematics (e.g. [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]); for concise recent reviews, see e.g.…”

“…d [42]. 35 Indeed, one can compute from the explicit hypergeometric solution (3.10) that S11 = − 1 2 csc πh 6 , using the monodromy of the hypergeometric functions (e.g. [38,85]).…”

Rational CFT with three characters: the quasi-character approach

“…However there is no reason to consider this a "typical" case. One of the fascinating developments of the last few years has been the generation of interesting results beyond = 0 [13,14,20,28,32,35]. By substituting the series expansion eq.…”

“…While quasi-characters do not directly correspond to any CFT, their linear combinations with semi-definite coefficients were shown to generate all admissible characters in order 2. In [32], many of these linear combinations were then shown to correspond to actual CFT.…”