D1/D5 system and Wilson Loops in (Non-)commutative Gauge Theories

TL;DR

This paper investigates Wilson loops in (5+1)-dimensional supersymmetric Yang-Mills theory using the D1/D5 string dual, revealing effects of solitons, D1-branes, and noncommutativity on potential behavior and area law emergence.

Contribution

It provides a detailed analysis of Wilson loops in the D1/D5 system, including velocity dependence, area law emergence, and noncommutative effects, extending understanding of gauge/string duality.

Findings

Velocity-dependent potential for temporal Wilson loops

Area law emergence due to D1-branes in spatial loops

Area law behavior in noncommutative gauge theories

Abstract

We study the behavior of the Wilson loop in the (5+1)-dimensional supersymmetric Yang-Mills theory with the presence of the solitonic object. Using the dual string description of the Yang-Mills theory that is given by the D1/D5 system, we estimate the Wilson loops both in the temporal and spatial cases. For the case of the temporal loop, we obtain the velocity dependent potential. For the spatial loop, we find that the area law is emerged due to the effect of the D1-branes. Further, we consider D1/D5 system in the presence of the constant B field. It is found that the Wilson loop obeys the area law for the effect of the noncommutativity.