The complex geometry of holographic flows of quiver gauge theories

Details The complex geometry of holographic flows of quiver gauge theories The complex geometry of holographic flows of quiver gauge theories

2004-06-17

arxiv.org/abs/hep-th/0406147v1

JHEP 0609 (2006) 063

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, harvmac + amssym

Scientific paper

10.1088/1126-6708/2006/09/063

We argue that the complete Klebanov-Witten flow solution must be described by a Calabi-Yau metric on the conifold, interpolating between the orbifold at infinity and the cone over T^(1,1) in the interior. We show that the complete flow solution is characterized completely by a single, simple, quasi-linear, second order PDE, or "master equation," in two variables. We show that the Pilch-Warner flow solution is almost Calabi-Yau: It has a complex structure, a hermitian metric, and a holomorphic (3,0)-form that is a square root of the volume form. It is, however, not Kahler. We discuss the relationship between the master equation derived here for Calabi-Yau geometries and such equations encountered elsewhere and that govern supersymmetric backgrounds with multiple, independent fluxes.

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