Probe D–branes in Superconformal Field Theories

The open/closed string descriptions of a system of Nc parallel D3–branes in flat space decouple in the large Nc limit, this leading to the duality between N = 4 supersymmetric Yang–Mills theory and type IIB string theory in AdS5 × S [1]. If, instead, the transverse six dimensional flat space background is replaced by a Calabi–Yau threefold, Y , the amount of preserved supercharges reduces to one quarter. 1 Provided Y 6 is a cone on a Sasaki–Einstein manifold X, and the stack of D3–branes is placed at the tip of the Calabi–Yau cone C(X), a duality between quiver N = 1 superconformal field theories (SCFT) and type IIB string theory in AdS5 ×X arises [4]. The case in which Y 6 is also toric, and X is topologically S ×S, is by now very well understood. There are three possibilities 2 (whose main features are displayed in Table 1):