Topological Conformal Algebra in $2d$ Gravity Coupled to Minimal Matter

Abstract

An infinite number of topological conformal algebras with varying central charges are explicitly shown to be present in $2d$ gravity (treated both in the conformal gauge and in the light-cone gauge) coupled to minimal matter. The central charges of the underlying $N=2$ theory in two different gauge choices are generically found to be different. The physical states in these theories are briefly discussed in the light of the $N=2$ superconformal symmetry.