Classification of Two-dimensional Rational Conformal Field Theories

Abstract

A complete understanding of the space of Conformal Field Theories is not yet available. However, a particular subclass called Rational Conformal Field Theories (RCFT’s) can be classified and understood using modular invariance. In this thesis, we review the formalism of classification of RCFT’s using the modular differential equations satisfied by their characters. This classification is based on two parameters n and \ell. The parameter n is the number of independent characters in the theory and \ell in an integer, the number of zeroes of the Wronskian of the characters. We study the classification of theories with low number of characters 1-4. The reconstruction of two-character theories from their characters is also discussed. We discuss the identification of two-character theories with \ell = 2 using our generalized coset construction. We use the same method to find new three and four-character theories with \ell = 0. For the new three and four character theories the degeneracies of the ground state are also calculated using our generalized coset construction.