Classification of RCFT from Holomorphic Modular Bootstrap: A Status Report

Abstract

Following the initial proposal in 1988, there has been much progress in classifying Rational Conformal Field Theories in 2 dimensions from the Holomorphic Bootstrap approach. This method starts by postulating a generic holomorphic Modular Linear Differential Equation of a given order and imposing the requirement of non-negative integrality of the coefficients in the series expansion of the solutions, which are then identified as admissible characters, from which a modular-invariant partition function is constructed. In this short note, the status of this project is summarised.

5 pages. To appear in the Proceedings of the Pollica Summer Workshop on "Mathematical and Geometric Tools for Conformal Field Theories'', June 3-21, 2019