Scattering of Open and Closed Strings in 1+1 Dimensions

TL;DR

This paper explores the algebraic structure of scattering amplitudes in 1+1 dimensional string theory, revealing recursion relations that uniquely determine open and closed tachyon interactions and potentially connect continuum models to matrix models.

Contribution

It introduces a novel algebraic framework based on the ground ring structure that derives recursion relations fixing scattering amplitudes uniquely.

Findings

Recursion relations among tachyon scattering amplitudes are derived.

The algebraic structure may connect continuum string theory to matrix models.

Associativity of the ring action determines all structure constants.

Abstract

The ground ring structure of 1+1 dimensional string theory leads to an infinite set of non linear recursion relations among the `bulk' scattering amplitudes of open and closed tachyons on the disk, which fix them uniquely. The relations are generated by the action of the ring on the tachyon modules; associativity of this action determines all structure constants. This algebraic structure may allow one to relate the continuum picture to a matrix model.