Penrose Limits and Non-local theories

We investigate Penrose limits of two classes of non-local theories, little string theories and non-commutative gauge theories. Penrose limits of the near-horizon geometry of NS5-branes help to shed some light on the high energy spectrum of little string theories. We attempt to understand renormalization group flow in these theories by considering Penrose limits wherein the null geodesic also has a radial component. In particular, we demonstrate that it is possible to construct a pp-wave spacetime which interpolates between the linear dilaton and the AdS regions for the Type IIA NS5-brane. Similar analysis is considered for the holographic dual geometry to non-commutative field theories.