Fundamental Strings and D-strings in the IIB Matrix Model

TL;DR

This paper investigates the IIB matrix model, showing its consistency with the double scaling limit, deriving a fundamental string vertex operator, and connecting D-strings with world sheet coordinates, highlighting the role of SL(2Z) duality.

Contribution

It presents a matrix model derivation of fundamental strings and D-strings, linking world sheet variables with D-string coordinates and elucidating the SL(2Z) duality group.

Findings

Large N perturbation is consistent with the double scaling limit.

A Wilson loop acts as a fundamental string vertex operator.

D-string boundary conditions are derived from the matrix model.

Abstract

The matrix model for IIB Superstring proposed by Ishibashi, Kawai, Kitazawa and Tsuchiya is investigated. Consideration of planar and non-planar diagrams suggests that the large N perturbative expansion is consistent with the double scaling limit proposed by the above authors. We write down a Wilson loop that can be interpreted as a fundamental string vertex operator. The one point tadpole in the presence of a D-string has the right form and this can be viewed as a matrix model derivation of the boundary conditions that define a D-string. We also argue that if world sheet coordinates $\sigma$ and $\tau$ are introduced for the fundamental string, then the conjugate variable ${d}/{d\sigma}$ and ${d}/{d\tau}$ can be interpreted as the D-string world sheet coordinates. In this way the $SL(2Z)$ duality group of the IIB superstring becomes identified with the symplectic group acting on ($p,q$).