The $W$ algebra structure of $N=2$ $CP_{n}$ coset models

TL;DR

This paper explores the structure of $N=2$ super $W$ algebras derived from affine Lie superalgebras, revealing free field realizations for $CP_n$ models and identifying twisted models as topological theories.

Contribution

It provides a new understanding of $N=2$ super $W$ algebras via hamiltonian reduction and characterizes certain models as topological conformal field theories.

Findings

Free field realization of $N=2$ $CP_n$ models obtained.

Models from $A(n|n)^{(1)}$ are twisted $N=2$ models.

Some models are identified as topological conformal field theories.

Abstract

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)