Novel Symmetries of Topological Conformal Field theories

Abstract

We show that various actions of topological conformal theories that were suggested recentely are particular cases of a general action. We prove the invariance of these models under transformations generated by nilpotent fermionic generators of arbitrary conformal dimension, $\Q$ and $\G$. The later are shown to be the $n^{th}$ covariant derivative with respect to ``flat abelian gauge field" of the fermionic fields of those models. We derive the bosonic counterparts $\W$ and $\mathbb{R}$ which together with $\Q$ and $\G$ form a special $N=2$ super $W_{\infty }$ algebra. The algebraic structure is discussed and it is shown that it generalizes the so called ``topological algebra".

26 pages