c=1 discrete states correlators via W$_{1+\infty}$ constraints

TL;DR

This paper computes genus zero correlators of discrete states in c=1 string theory at the self-dual radius using W_{1+ abla} constraints, revealing an integrable structure and deriving the dilaton equation.

Contribution

It introduces an iterative method to derive current dependencies on couplings and connects the correlators to the integrable structure of the theory.

Findings

Genus zero correlators are explicitly computed.

An analogy with integrable structures is established.

The dilaton equation for the theory is derived.

Abstract

The discrete states of $c=1$ string theory at the self-dual radius are associated with modes of $W_{1+\infty}$ currents and their genus zero correlators are computed. An analogy to a recent suggestion based on the integrable structure of the theory is found. An iterative method for deriving the dependence of the currents on the full space of couplings is presented and applied. The dilaton equation of the theory is derived.