Superstring Theory on pp Waves with ADE Geometries

We study the BMN correspondence between certain Penrose limits of type IIB superstrings on pp-wave orbifolds with $ADE$ geometries, and the set of four-dimensional $\mathcal{N}=2$ superconformal field theories constructed as quiver gauge models classified by finite $ADE$ Lie algebras and affine $\hat{ADE}$ Kac-Moody algebras. These models have 16 preserved supercharges and are based on systems of D3-branes and wrapped D5- and D7-branes. We derive explicitly the metrics of these pp-wave orbifolds and show that the BMN extension requires, in addition to D5-D5 open strings in bi-fundamental representations, D5-D7 open strings involving orientifolds with $Sp(N)$ gauge symmetry. We also give the correspondence rule between leading string states and gauge-invariant operators in the $\mathcal{N}=2$ quiver gauge models.