On Moduli Space of C=0 Topological Conformal Field Theories

TL;DR

This paper explores the structure and relationships within the moduli space of c=0 topological conformal field theories, identifying a unified family of models and proposing a new classification for an N=2 TCFT.

Contribution

It demonstrates that several key c=0 TCFTs form a single parameter family and conjectures a separate family for an N=2 TCFT from Wolf space realization.

Findings

Topological SL(2) WZW model, superconformal ghost system, and N=2 TCFT belong to the same moduli space.

Identified a potential second family of c=0 TCFTs related to N=4 superconformal algebra.

Unified description of multiple models within the moduli space.

Abstract

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.