Towards a classification of two-character rational conformal field theories

Abstract

We provide a simple and complete construction of infinite families of consistent, modular-covariant pairs of characters satisfying the basic requirements to describe twocharacter RCFT. These correspond to solutions of generic second-order modular linear differential equations. To find these solutions, we first construct "quasi-characters" from the Kaneko-Zagier equation and subsequent works by Kaneko and collaborators, together with coset dual generalisations that we provide in this paper. We relate our construction to the Hecke images recently discussed by Harvey and Wu.

Rationalizing CFTs and anyonic imprints on Higgs branches

“…41 Perhaps these can be related to rational theories after turning on some flavor fugacities (or, 41 This statement can be easily seen by considering the linear modular differential equations (LMDEs) satisfied by the Schur index (e.g., see [52] for an introduction in the context of the 4D/2D correspondence of [2]). For other interesting recent work on LMDEs and their implications for 2D CFT, see [66,67]. more generally, fugacities for generators corresponding to a unitary W -algebra).…”

“…Perhaps the recent notion of Galois conjugation at the level of RCFT characters [42] will prove useful to make contact between the UV and IR. The LMDE-based discussion in [66] may also play a role.…”

Curiosities above c = 24

“…The case of ℓ = 4, discussed in [15] is somewhat enigmatic: this reference found precisely three new admissible pairs of characters but no concrete construction of a corre-sponding CFT is known so far 3 . The case of ℓ ≥ 6 presents interesting new features.…”

“…Let us briefly review the classification method and some new results which will be relevant for our discussion. A detailed review with several new results can be found in [15]. We limit ourselves to the case of two characters, which is all we will be using in this paper.…”

“…There are various checks to ensure that these coefficients retain integrality and a definite sign asymptotically. The resulting solutions fall into two classes: the admissible characters where all the coefficients are non-negative, and quasi-characters [15] where the first few coefficients are allowed to be negative integers. For the admissible case, one tries to reconstruct the CFT corresponding to these characters, if it exists [2,3,17].…”