Wilson Loops in Noncommutative Yang Mills

TL;DR

This work embeds noncommutative Yang-Mills within twisted reduced models derived from the IIB matrix model and analyzes gauge-invariant Wilson-loop correlators. It reveals a crossover at the noncommutativity scale $\lambda$: at high momentum the theory behaves like large-$N$ Yang-Mills with planar dominance, while at low momentum NCYM reduces to ordinary YM; the NCYM coupling $g^2_{NC}$ coincides with the high-energy 't Hooft coupling. The authors apply these results to D-brane backgrounds to connect NCYM with four-dimensional $\mathcal{N}=4$ SYM and discuss consistency with supergravity descriptions featuring running dilaton, as well as a Seiberg-Witten map between different star-product descriptions. Overall, the paper argues for a unified, nonperturbative framework in which NCYM, twisted reduced models, D-brane dynamics, and SW dual descriptions coherently describe gauge dynamics across energy scales and relate to gravity duals.

Abstract

We study the correlation functions of the Wilson loops in noncommutative Yang-Mills theory based upon its equivalence to twisted reduced models. We point out that there is a crossover at the noncommutativity scale. At large momentum scale, the Wilson loops in noncommmutative Yang-Mills represent extended objects. They coincide with those in ordinary Yang-Mills theory in low energy limit. The correlation functions on D-branes in IIB matrix model exhibit the identical crossover behavior. It is observed to be consistent with the supergravity description with running string coupling. We also explain that the results of Seiberg and Witten can be simply understood in our formalism.