Updating the holomorphic modular bootstrap

TL;DR

This paper advances the holomorphic modular bootstrap by incorporating recent exact S-matrix computations within MLDEs, identifying admissible solutions with potential CFT interpretations.

Contribution

It updates the bootstrap framework with new S-matrix results, classifies admissible MLDE solutions with specific constraints, and links them to known CFTs and MTC classes.

Findings

Computed exact S-matrix within MLDE setting.

Classified admissible solutions with up to six characters and specific Wronskian index.

Identified solutions with good fusion rules and associated them with known CFTs.

Abstract

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.