The holomorphic modular bootstrap for classifying Rational Conformal Field Theories(RCFT) can be done using the Modular Linear Differential Equation (MLDE) and Vector Valued Modular Form (VVMF) approaches. I will explain MLDEs and how we can solve MLDEs with up to one accessory parameter and Wronskian index <6 to obtain admissible solutions. Further, I show how the modular S-matrix can be obtained numerically within the MLDE framework and how it leads to an exact expression. Using a combination of Hecke operators, GHM duality, Involutive duality and/or the known S-matrix, we will fix an ambiguity in degeneracy in the MLDE solution. In the VVMF perspective, quasi-characters, which arise as solutions to a matrix MLDE, are used to construct new admissible solutions with Wronskian index >=6. We show that these multiple perspectives provide a systematic framework to construct admissible solutions with up to six characters and arbitrary Wronskian index.
Zoom link: https://icts-res-in.zoom.us/j/88092766911?pwd=R3ZrVk9yeW96ZmQ4ZG9KRzVhenRKZz09
Meeting ID: 880 9276 6911
Passcode: 232322