The PP-Wave Limits of Orbifolded AdS_5x S^5

TL;DR

This paper investigates two types of pp-wave limits of orbifolded AdS spaces, revealing cases with and without supersymmetry enhancement, and identifies corresponding operators in the dual gauge theories.

Contribution

It identifies two distinct pp-wave limits of orbifolded AdS spaces and connects them to supersymmetry properties and dual gauge theory operators.

Findings

One pp-wave limit is an orbifold of the maximally supersymmetric case.

The other pp-wave limit retains maximal supersymmetry.

Operators in ${ m f N}=2$ gauge theory correspond to string excitations in the orbifolded geometry.

Abstract

Using the supergravity solution of $N_1$ D3-branes probing $A_{N_2-1}$ singularities we study the pp-wave limit of $AdS_5\times S^5/Z_{N_2}$. We show that there are two different pp-wave limits. One is the orbifold of the pp-wave limit of $AdS_5\times S^5$. In this case there is no symmetry enhancement. The other case is the same as the pp-wave limit of $AdS_5\times S^5$ and therefore we again see the maximal supersymmetry. We will also identify operators in the four dimensional ${\cal N}=2$ $SU(N_1)^{N_2}$ gauge theory which correspond to stringy excitations in the orbifolded pp-wave geometry. The existence of the maximal pp-wave geometry indicates that there is a subsector of the corresponding ${\cal N}=2$ gauge theories which has enhanced ${\cal N}=4$ supersymmetry. We also study the pp-wave limits of $AdS_{7,4}\times S^{4,7}/Z_{N}$.