Non-commutative Yang-Mills and the AdS/CFT correspondence

Abstract

We study the non-commutative supersymmetric Yang-Mills theory at strong coupling using the AdS/CFT correspondence. The supergravity description and the UV/IR relation confirms the expectation that the non-commutativity affects the ultra-violet but not the infra-red of the Yang-Mills dynamics. We show that the supergravity solution dual to the non-commutative N = 4 SYM in four dimensions has no boundary and defines a minimal scale. We also show that the relation between the B field and the scale of non-commutativity is corrected at large coupling and determine its dependence on the 't Hooft coupling λ. July 1999Classical supersymmetric Yang-Mills theory (SYM) in (p + 1)-dimensional space can be generalized to SYM on non-commutative spaces [1]. Since the generalization involves infinitely many higher order terms, it is very hard to provide a pure field theory proof that such a theory is consistent at the quantum level. String theory provides a way to obtain these theories by considering the decoupling limit of D(p−2)-branes in type II string theories on T 2 with a background NSNS 2-form field B µν polarized along the plane of the torus [2,3]. The fact that non-commutative SYM is obtained from string theory, in a limit which does not involve gravity, suggests (if string theory with constant B field is consistent) that the non-commutative SYM, at least with sixteen supercharges, is a consistent theory at the quantum level.

Noncommutative brane-world, (Anti) de Sitter vacua and extra dimensions

“…Following the prescription, we consider the brane as the boundary of the AdS 5 geometry. In fact, the interpretation has been shown to be in precise agreement with the AdS/ noncommutative gauge theory correspondence [23,24,25]. The induced metric g µν on the boundary ∂M is not completely constant, rather it takes into account the dynamical aspects of gravity in the bulk M. In other words, the boundary dynamics is not independent of that in the string bulk.…”

DBI from gravity

“…Specifically, T-duality can be used to generate constant magnetic or electric fields from toroidal metric configuration with off-diagonal metric terms. This approach was used in [11] to generate deformed Taub-NUT solutions with magnetic fields, following the earlier work of [30,31] in the context of other branes with background fluxes.…”

On non-commutative super Yang–Mills

“…At one loop, these effects appear only in amplitudes which involve external legs in the center of the gauge group [19]. For N = 4 theory theses effects cancel [4] and in the infrared the theory converges to the ordinary one [5,6].…”