1+1 Dimensional NCOS and its U(N) Gauge Theory Dual

TL;DR

This work analyzes 1+1 dimensional non-commutative open string theory (NCOS) in a critical electric-field background and establishes a precise duality to $U(N)$ maximally supersymmetric Yang–Mills theory with electric flux. The authors derive the parameter map $G_0^2 = 1/N$ and $g_{YM}^2 = N^2/ obreak\alpha'_e$ (extendable to $G_0^2 = M/N$, $g_{YM}^2 = N^2/(M^2 \alpha'_e)$ for flux $M$) and demonstrate that the $U(1)$ sector decouples, matching the gauge theory expectation of a free $U(1)$ factor with a mass gap in the $SU(N)/\mathbb{Z}_N$ sector. Upon compactifying the electric-field direction, the theory exhibits wound closed strings with tension $T_{wound} = 1/(4\pi \alpha'_e)$ whose spectrum aligns with Higgs-branch excitations, and nonplanar diagrams reveal closed-string poles consistent with the dual description. These results provide robust evidence for the NCOS/$U(N)$ SYM duality and illuminate connections to Matrix-string theory and DLCQ descriptions of IIA string theory.

Abstract

We study some aspects of open string theories on D-branes with critical electric fields. We show that the massless open string modes that move in the direction of the electric field decouple. In the 1+1 dimensional case the dual theory is U(N) SYM with electric flux, and the decoupling of massless open strings is dual to the decoupling of the U(1) degrees of freedom. We also show that, if the direction along the electric field is compact, then there are finite energy winding closed string modes. They are dual to Higgs branch excitations of the SYM theory, and their energetics works accordingly. These properties provide new non-trivial evidence for the duality.

Figures (1)

• Figure 1: Nonplanar open string diagram. In open string field theory we would build it from the cubic vertex and we would consider states carrying momentum $q$ and $q+p$ along the loop.