Large N Limit of Non-Commutative Gauge Theories

TL;DR

This paper explores the large N limit of non-commutative gauge theories using gravity duals, revealing that degrees of freedom match the commutative case and analyzing correlation functions and string configurations.

Contribution

It provides new insights into the degrees of freedom and string behavior in non-commutative gauge theories at large N using holographic methods.

Findings

Degrees of freedom match the commutative case at any scale.

Two-point functions decay exponentially in the UV regime.

Existence of worldsheet instantons localized in finite regions.

Abstract

Using the correspondence between gauge theories and string theory in curved backgrounds, we investigate aspects of the large $N$ limit of non-commutative gauge theories by considering gravity solutions with $B$ fields. We argue that the total number of physical degrees of freedom at any given scale coincides with the commutative case. We then compute a two-point correlation function involving momentum components in the directions of the $B$-field. In the UV regime, we find that the two-point function decays exponentially with the momentum. A calculation of Wilson lines suggests that strings cannot be localized near the boundary. We also find string configurations that are localized in a finite region of the radial direction. These are worldsheet instantons.