ON TOPOLOGICAL $2D$ STRING AND INTERSECTION THEORY

TL;DR

This paper explores the topological and intersection theory aspects of 2D string theory at the self-dual radius, revealing discrepancies between string correlators and intersection numbers due to negative momentum tachyons.

Contribution

It provides an algebro-geometrical formulation of 2D string theory using $A_{k+1}$ models at $k=-3$, and analyzes the impact of negative momentum tachyons on correlation functions.

Findings

Computed genus zero correlators as intersection numbers on moduli space.

Identified a disagreement between 2D string correlators and intersection numbers.

Interpreted negative momentum tachyons as gravitational descendants of the cosmological constant.

Abstract

The topological description of $2D$ string theory at the self-dual radius is studied in the algebro-geometrical formulation of the $A_{k+1}$ topological models at $k=-3$. Genus zero correlators of tachyons and their gravitational descendants are computed as intersection numbers on moduli space and compared to $2D$ string results. The interpretation of negative momentum tachyons as gravitational descendants of the cosmological constant, as well as modifications of this, is shown to imply a disagreement between $2D$ string correlators and the associated intersection numbers.