Remarks on the Physical States and the Chiral Algebra of 2D Gravity Coupled to $C \leq 1$ Matter

TL;DR

This paper explores the structure of physical states and the chiral algebra in 2D gravity coupled to matter with central charge less than or equal to one, revealing the algebra's role as a general symmetry across models.

Contribution

It demonstrates that the $w_{ty}$ chiral algebra is realized in both $C q 1$ and minimal models of 2D gravity, establishing it as a universal symmetry.

Findings

Chiral algebra $w_{ty}$ is present in $C q 1$ matter models.

The algebra also appears in minimal models with $C < 1$.

The results suggest a universal symmetry in 2D gravity theories.

Abstract

Some elaboration is given to the structure of physical states in 2D gravity coupled to $C \leq 1$ matter, and to the chiral algebra ($w_{\infty}$) of $C_{M} = 1$ theory which has been found recently, in the continuum approach, by Witten and by Klebanov and Polyakov. It is shown then that the chiral algebra is being realized as well in the minimal models of gravity ($C_{M}<1$), so that it stands as a general symmetry of 2D gravity theories.