On Penrose limit of elliptic branes

We discuss a Penrose limit of an elliptic brane configuration with $N_1$ NS5and $N_2$ D4 branes. This background is T-dual to $N_1$ D3 branes at a fixedpoint of a $\mathbf{C}^3/\mathbf{Z}_{N_2}$ singularity and the T-dualitysurvives the Penrose limit. The triple scaling limit of $N_1$ and $N_2$ givesrise to IIA pp-wave solution with a space-like compact direction. We identifythe quiver gauge theory operators and argue that upon exchange of the momentumalong the compact direction and the winding number these operators coincidewith the operators derived in the dual type IIB description. We also find a newPenrose limit of the type IIB background and the corresponding limit in thetype IIA picture. In the coordinate system we use there are two manifestspace-like isometries. The quiver gauge theory operator duals of the stringstates are built of three bosonic fields.Comment: 25 pages with 1 figur