Supersymmetric double-well matrix model as two-dimensional type IIA superstring on RR background

TL;DR

This paper demonstrates a detailed correspondence between a supersymmetric double-well matrix model and two-dimensional type IIA superstring theory on a Ramond-Ramond background by comparing scattering amplitudes and establishing precise quantitative relations.

Contribution

It provides a dynamical verification of the matrix model and string theory correspondence through explicit amplitude calculations and coefficient relations.

Findings

Matching scattering amplitudes in both theories.

Quantitative agreement of parameter dependence.

Relations among coefficients confirming the correspondence.

Abstract

In the previous paper, the authors pointed out correspondence of a supersymmetric double-well matrix model with two-dimensional type IIA superstring theory on a nontrivial Ramond-Ramond background from the viewpoint of symmetries and spectrum. In this paper we further investigate the correspondence from dynamical aspects by comparing scattering amplitudes in the matrix model and those in the type IIA theory. In the latter, cocycle factors are introduced to vertex operators in order to reproduce correct transformation laws and target-space statistics. By a perturbative treatment of the Ramond-Ramond background as insertions of the corresponding vertex operators, various IIA amplitudes are explicitly computed including quantitatively precise numerical factors. We show that several kinds of amplitudes in both sides indeed have exactly the same dependence on parameters of the theory. Moreover, we have a number of relations among coefficients which connect quantities in the type IIA theory and those in the matrix model. Consistency of the relations convinces us of the validity of the correspondence.