Supergravity Duals to the Noncommutative N=4 SYM theory in the Infinite Momentum Frame

Abstract

In this work the construction of supergravity duals to the noncommutative ${\cal N}=4$ SYM theory in the infinite momentum frame but with constant momentum density is attempted. In the absence of the content of noncommutativity, it has been known for some time that the previous $AdS_{5}/CFT_{4}$ correspondence should be replaced by the $K_{5}/CFT_{4}$ (with $K_{(p+2)}$ denoting the generalized Kaigorodov spacetime) correspondence with the pp-wave propagating on the BPS brane worldvolume. Interestingly enough, putting together the two contents, i.e., the introduction of noncommutativity and at the same time that of the pp-wave along the brane worldvolume, leads to quite nontrivial consequences such as the emergence of ``time-space'' noncommutativity in addition to the ``space-space'' noncommutativity in the manifold on which the dual gauge theory is defined. Taking the gravity decoupling limit, it has been realized that for small $u$, the solutions all reduce to $K_{5}\times S^5$ geometry confirming our expectation that the IR dynamics of the dual gauge theory should be unaffected by the noncommutativity while as $u\to \infty$, the solutions start to deviate significantly from $K_{5}\times S^5$ limit indicating that the UV dynamics of the dual gauge theory would be heavily distorted by the effect of noncommutativity.