On Penrose limit of elliptic branes

TL;DR

This paper explores the Penrose limit of elliptic brane configurations, revealing connections between IIA and IIB backgrounds, and identifies dual gauge theory operators with string states in these limits.

Contribution

It introduces a novel Penrose limit of elliptic branes, establishing dualities between different string backgrounds and their gauge theory operators.

Findings

Identification of IIA pp-wave solution with space-like compact direction.

Matching of gauge theory operators with string states under dualities.

Discovery of a new Penrose limit in IIB background.

Abstract

We discuss a Penrose limit of an elliptic brane configuration with $N_1$ NS5 and $N_2$ D4 branes. This background is T-dual to $N_1$ D3 branes at a fixed point of a $\mathbf{C}^3/\mathbf{Z}_{N_2}$ singularity and the T-duality survives the Penrose limit. The triple scaling limit of $N_1$ and $N_2$ gives rise to IIA pp-wave solution with a space-like compact direction. We identify the quiver gauge theory operators and argue that upon exchange of the momentum along the compact direction and the winding number these operators coincide with the operators derived in the dual type IIB description. We also find a new Penrose limit of the type IIB background and the corresponding limit in the type IIA picture. In the coordinate system we use there are two manifest space-like isometries. The quiver gauge theory operator duals of the string states are built of three bosonic fields.