Applications of Current Algebra in Conformal Field Theory

In this work, two topics concerning the interplay between current algebra and conformal symmetry in two dimensions are discussed. The construction of a conformal algebra from a current algebra, the Virasoro master equation, is presented with analytic and perturbative solutions. Second, N = 2 superconformal models based on supersymmetric current algebras with c > 3 are coupled to two dimensional topological gravity.