Wilson loops in noncommutative Yang–Mills theory using gauge/gravity duality

Abstract

By using the gauge/gravity duality and the Maldacena prescription we compute the expectation values of the Wilson loops in hot, noncommutative Yang–Mills (NCYM) theory in (3+1) dimensions. We consider both the time-like and the light-like Wilson loops. The gravity dual background is given by a particular decoupling limit of non-extremal (D1, D3) bound state of type IIB string theory. We obtain the velocity dependent quark–antiquark potential and numerically study how the dipole length and the potential change with velocity (for 0<v<1, i.e., the Wilson loop is time-like) of the dipole as well as noncommutativity. We discuss and compare the results with the known commutative results. We also obtain an analytic expression for the screening length when the rapidity is large and the noncommutativity parameter is small with the product remaining small. When v→1, the time-like Wilson loop becomes light-like and in that case we obtain the form of the jet quenching parameter for the strongly coupled noncommutative Yang–Mills plasma which matches with our earlier results obtained using different approach.