Gravitational Scattering in the c = 1 Matrix Model

TL;DR

This paper demonstrates how a nonlocal field redefinition transforms the local $c=1$ matrix model interaction into the nonlocal string theory form, revealing gravitational effects in scattering processes.

Contribution

It shows how to convert the local matrix model interaction into the nonlocal string theory interaction using a specific field redefinition, clarifying the role of gravity.

Findings

Nonlocal field redefinition maps matrix model to string theory interactions.

Asymptotic gravitational behavior is observed in scattering.

The approach clarifies the relation between matrix model and string theory.

Abstract

The $c=1$ matrix model is equivalent to $1+1$ dimensional string theory. However, the tachyon self-interaction in the former is local, while in the latter it is nonlocal due to the gravitational, dilaton and higher string fields. By studying scattering of classical pulses we show that the appropriate nonlocal field redefinition converts the local matrix model interaction into the expected string form. In particular, we see how the asymptotic behavior of the gravitational field appears in the scattering.