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 N = 2 superconformal field theories constructed as quiver gauge models classified by finite ADE Lie algebras and affine 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 N = 2 quiver gauge models.
Using the Iqbal-Netzike-Vafa dictionary giving the correspondence between the H 2 homology of del Pezzo surfaces and p-branes, we develop a way to approach the system of brane bounds in M-theory on S 1 . We first review the structure of 10-dimensional quantum Hall soliton ͑QHS͒ from the view of M-theory on S 1 . Then, we show how the D0 dissolution in D2-brane is realized in M-theory language and derive the p-brane constraint equations used to define appropriately the QHS. Finally, we build an algebraic geometry realization of the QHS in type IIA superstring and show how to get its type IIB dual. Other aspects are also discussed.
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