On Moduli Space of C=0 Topological Conformal Field Theories

We studied the marginal deformation of the $c=0$ topological conformal field theories (TCFT). We showed that topological $SL(2)$ Wess-Zumino-Witten (WZW) model, topological superconformal ghost system, TCFT constructed from the $N=2$ superconformal system and two dimensional topological gravity belong to the same one parameter family (moduli space) of the $c=0$ TCFT's. We conjectured that the $N=2$ TCFT constructed from the Wolf space realization of $N=4$ superconformal algebra belongs to another family.