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.
