We discuss the $N=2$ super $W$ algebras from the hamiltonian reduction of affine Lie superalgebras $A(n|n-1)^{ (1)}$ and $A(n|n)^{ (1)}$. From the quantum hamiltonian reduction of $A(n|n-1)^{ (1)}$ we get the free field realization of $N=2$ $CP_{ n}$ super coset models. In the case of the affine Lie superalgebras $A(n|n)^{ (1)}$, the corresponding conformal field theories do not have $N=2$ superconformal symmetry. However we show that these models are twisted $N=2$ $CP_{ n}$ models and may be regarded as topological conformal field theories. (Talk presented at the International Workshop on "String Theory, Quantum Gravity and the Unification of Fundamental Interactions" Rome, September 21--26, 1992)
Categories: hep-th