Classifying three-character RCFTs with Wronskian index equalling 0 or 2

A bstract In the modular linear differential equation (MLDE) approach to classifying rational conformal field theories (RCFTs) both MLDE and RCFT are identified by a pair of non-negative integers [n,l] . n is number characters as well order that solve l , Wronskian index, associated structure zeroes characters. this paper, we study [3,0] [3,2] MLDEs in classify corresponding CFTs. We reduce problem “finite” problem: CFTs with central charge 0 < c ? 96, need perform 6 720 computations for former 20 160 latter. Each computation involves (i) first finding simultaneous solution Diophantine equations (ii) computing Fourier coefficients high checking positivity. case, obtain many character-like solutions: two infinite classes discrete set 303. After accounting various categories known solutions, including Virasoro minimal models, WZW CFTs, Franc-Mason vertex operator algebras Gaberdiel-Hampapura-Mukhi novel coset seem have seven hitherto unknown solutions which could potentially give new also 96: each CFT case obtained adjoining constant character [2,0] CFT, whose classification was achieved Mathur-Mukhi-Sen three decades ago.