Holographic Noncommutativity

We examine noncommutative Yang-Mills and open string theories using magnetically and electrically deformed supergravity duals. The duals are near horizon regions of Dp-brane bound state solutions which are obtained by using O(p+1,p+1) transformations of Dp-branes. The action of the T-duality group implies that the noncommutativity parameter is constant along holographic RG-flows. The moduli of the noncommutative theory, i.e., the open string metric and coupling constant, as well as the zero-force condition are shown to be invariant under the O(p+1,p+1) transformation, i.e., deformation independent. We find sufficient conditions, including zero force and constant dilaton in the ISO(3,1)-invariant D3 brane solution, for exact S-duality between noncommutative Yang-Mills and open string theories. These results are used to construct noncommutative field and string theories with N=1 supersymmetry from the T^(1,1) and Pilch-Warner solutions. The latter has a non-trivial zero-force condition due to the warping.Comment: latex, 40 pp. v2: minor changes, one ref. added. v3: corrections in eqs. 27 and 7

Göteborg ITP preprint

Abstract: We examine noncommutative Yang–Mills and open string theories using magnetically and electrically deformed supergravity duals. The duals are near horizon regions of Dp-brane bound state solutions which are obtained by using O(p+1,p+1) transformations of Dp-branes. The action of the T-duality group implies that the noncommutativity parameter is constant along holographic RG-flows. The moduli of the noncommutative theory, i.e., the open string metric and coupling constant, as well as the zero-force condition are shown to be invariant under the O(p +1,p+1) transformation, i.e., deformation independent. We find sufficient conditions, including zero force and constant dilaton in the ISO(3, 1)-invariant D3 brane solution, for exact S-duality between noncommutative Yang–Mills and open string theories. These results are used to construct noncommutative field and string theories with N = 1 supersymmetry from the T (1,1) and Pilch–Warner solutions. The latter has a non-trivial zero-force condition due to the warping