Bootstrapping fermionic rational CFTs with three characters

Abstract

Recently, the modular linear differential equation (MLDE) for level-two congruence subgroups Γθ, Γ0(2) and Γ0(2) of SL2(ℤ) was developed and used to classify the fermionic rational conformal field theories (RCFT). Two character solutions of the second-order fermionic MLDE without poles were found and their corresponding CFTs are identified. Here we extend this analysis to explore the landscape of three character fermionic RCFTs obtained from the third-order fermionic MLDE without poles. Especially, we focus on a class of the fermionic RCFTs whose Neveu-Schwarz sector vacuum character has no free-fermion currents and Ramond sector saturates the bound hR ≥ $$ \frac{C}{24} $$ C 24 , which is the unitarity bound for the supersymmetric case. Most of the solutions can be mapped to characters of the fermionized WZW models. We find the pairs of fermionic CFTs whose characters can be combined to produce K(τ), the character of the c = 12 fermionic CFT for Co0 sporadic group.

Fermionic Rational Conformal Field Theories and Modular Linear Differential Equations

“…Specifically, the solution with c = 11 exhibits moonshine phenomena for the Suzuki group as shown in [27]. Further examples of fermionic deconstructions will be discussed in an upcoming paper [28].…”

“…This can be shown with the help of a rank 21 lattice that constructed in [47]. We will discuss more details of this theory in an upcoming paper [28].…”

“…The automorphism group of N = 1 SVOA with c = 11 is known as the Suzuki group, which is one of the maximal subgroup of Co 0 . It would be interesting to investigate further deconstruction examples of c = 12 superconformal theory, and the details will be discussed in an upcoming paper [28].…”

Needles in a haystack: An algorithmic approach to the classification of 4d $\mathcal{N}=2$ SCFTs

“…A corollary of this conjecture is that any VOA with a 4d avatar is "quasi-lisse", 6 and as such its vacuum character must satisfy a monic modular differential equation (MDE) [37]. 7 Depending on whether we require modular invariance under the full modular group or just an index two subgroup [23,43,44], an MDE is called respectively untwisted or twisted. The space of possible MDEs is labelled by a finite set of real parameters, the number of which depends only on the degree of the differential equation and whether it is untwisted or twisted.…”

“…In the context of 2d CFT, this idea goes back to the classic work of Mathur, Mukhi, and Sen [45][46][47], see e.g. [43,44,[48][49][50][51][52][53][54][55][56][57][58][59][60][61] for recent developments. As scanning over the set of real numbers parameterizing the MDE would clearly be impossible, our first step is to map the problem to a scan over integers.…”