Long String Scattering in c = 1 String Theory

TL;DR

This paper investigates long string scattering in c=1 string theory through worldsheet and matrix model perspectives, computing amplitudes and confirming duality with numerical agreement.

Contribution

It provides the first detailed calculation of long string scattering amplitudes from open string decoupling limits and confirms duality predictions with numerical evidence.

Findings

Long string scattering amplitudes are well-defined as open string limits.

Results show strong numerical agreement with dual matrix model computations.

Provides evidence supporting the duality between string theory and matrix models.

Abstract

We study the scattering of long strings in c = 1 string theory, both in the worldsheet description and in the non-singlet sector of the dual matrix quantum mechanics. From the worldsheet perspective, the scattering amplitudes of long strings are obtained from a decoupling limit of open strings amplitudes on FZZT branes, which we compute by integrating Virasoro conformal blocks along with structure constants of boundary Liouville theory. In particular, we study the tree level amplitudes of (1) a long string decaying by emitting a closed string, and (2) the scattering of a pair of long strings. We show that they are indeed well defined as limits of open string amplitudes, and that our results are in striking numerical agreement with computations in the adjoint and bi-adjoint sectors of the dual matrix model (based on proposals of Maldacena and solutions due to Fidkowski), thereby providing strong evidence of the duality.