Updating the holomorphic modular bootstrap

A bstract We update the holomorphic modular bootstrap incorporating a recent result that computes the exact S -matrix within the Modular Linear Differential Equation (MLDE) setting. Further, using knowledge of the allowed exponents modulo one, we obtain admissible solutions to all MLDE’s with up to six characters and Wronskian index < 6 and one accessory parameter with c eff ≤ 24. We then identify which of the admissible solutions have good fusion rules — we call such solutions tenable . When possible, we identify the CFT and in the unitary cases the MTC class they belong to.