Green-Schwarz superstring from type IIB matrix model

Abstract

We construct Green-Schwarz (GS) light-cone closed superstring theory from type IIB matrix model. A GS light-cone string action is derived from two dimensional N=8 U(n) noncommutative Yang-Mills (NCYM) by identifying noncommutative scale with string scale. Supersymmetry transformation for the light-cone gauge action is also derived from supersymmetry transformation for IIB matrix model. By identifying the physical states and interaction vertices, string theory is perturbatively reproduced.Comment: 5 pages, 3 figures, minor revision

Superstring vertex operators in type IIB matrix model

“…Since there are no scale parameters in the action of IIB matrix model, the noncommutativity could provide a fundamental scale in the emergent theory. We have indeed identified the scale in NC gauge theory with the string scale in the previous paper [5]. Since the NC scale sets the eigenvalue density of the matrices, our identification of the string scale is consistent with [9].…”

“…Dijkgraaf, Verlinde and Verlinde have shown that the IR limit corresponds to the free string limit. This logic is applicable to our case and actually we have derived the free Green-Schwarz string action from NC gauge theory by taking the strong coupling limit [5]. We emphasize here that the strong coupling limit (the IR limit) of NC gauge theory is the free string limit, not the low energy limit of Green-Schwarz string theory.…”

“…In section II B, we review the closed superstring vertex operator construction of GS light-cone superstring theory. In section II C, we review the derivation of GS lightcone superstring action from IIB matrix model, which is carried out in the previous paper [5]. The derivation of supersymmetry transformation for GS light-cone superstring from IIB matrix model is also shown.…”

“…String theory is perturbatively reproduced from type IIB matrix model [1] via two dimensional noncommutative (NC) N = 8 supersymmetric gauge theory [2,3,4] in the IR limit [5]. The emergent string theory is GreenSchwarz (GS) type IIA superstring theory with light-cone gauge [6], which is also derived from commutative N = 8 super Yang-Mills [7].…”

“…As we have derived supersymmetry transformation of GS light-cone superstring from IIB matrix model on the two dimensional backgrounds [5], we can reconstruct the superstring vertex operators based on the symmetry. In such a sense, this comparison can be regarded as a consistency check of the IIB matrix model vertex operator construction.…”