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

TL;DR

This paper demonstrates the existence of an infinite family of topological conformal algebras with different central charges in two-dimensional gravity coupled to minimal matter, highlighting gauge-dependent variations in the underlying N=2 theory.

Contribution

It explicitly constructs and analyzes topological conformal algebras with varying central charges in 2D gravity coupled to minimal matter, revealing gauge-dependent differences in N=2 theories.

Findings

Presence of infinite topological conformal algebras in 2D gravity

Central charges vary with gauge choice in N=2 theories

Discussion of physical states within the N=2 superconformal framework

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.