Factorization and Topological States in $c=1$ Matter Coupled to 2-D Gravity

TL;DR

This paper explores the factorization of N-point amplitudes in two-dimensional c=1 quantum gravity, highlighting the role of short-distance singularities and the contribution of topological states beyond tachyons.

Contribution

It provides a detailed analysis of how topological states influence amplitude factorization in c=1 quantum gravity coupled to matter and 2D gravity.

Findings

Factorization linked to operator product expansion and Liouville zero mode integration.

Identification of infinite topological states contributing to intermediate states.

Insights into the structure of amplitudes in 2D quantum gravity.

Abstract

Factorization of the $N$-point amplitudes in two-dimensional $c=1$ quantum gravity is understood in terms of short-distance singularities arising from the operator product expansion of vertex operators after the Liouville zero mode integration. Apart from the tachyon states, there are infinitely many topological states contributing to the intermediate states.