Supergravity Dual of Noncommutative N=1 SYM

TL;DR

This paper constructs a supergravity dual of noncommutative N=1 SYM, revealing confinement, UV/IR mixing, and matching beta-functions with the commutative case, thus extending gauge/gravity duality to noncommutative theories.

Contribution

It introduces a noncommutative deformation of the Maldacena-Nunez solution, providing a gravity dual for noncommutative N=1 SYM with detailed analysis of IR confinement and UV/IR mixing.

Findings

Demonstrates confinement in the IR via Wilson loop calculations.

Shows UV/IR mixing effects are visible in the supergravity solution.

Confirms the beta-function matches the commutative N=1 SYM case.

Abstract

We construct the noncommutative deformation of the Maldacena-Nunez supergravity solution. The background describes a bound state of D5-D3 branes wrapping an S^2 inside a Calabi-Yau three-fold, and in the presence of a magnetic B-field. The dual field theory in the IR is a N=1 U(N) SYM theory with spatial noncommutativity. We show that, under certain conditions, the massive Kaluza-Klein states can be decoupled and that UV/IR mixing seems to be visible in our solution. By calculating the quark-antiquark potential via the Wilson loop we show confinement in the IR and strong repulsion at closer distances. We also compute the beta-function and show that it coincides with the recently calculated commutative one.