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The complex geometry of holographic flows of quiver gauge theories

Nick Halmagyi·Krzysztof Pilch·Christian Romelsberger·Nicholas P. Warner
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Abstract

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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Nick Halmagyi, Krzysztof Pilch, Christian Romelsberger, Nicholas P. Warner. 2004-06-17. The complex geometry of holographic flows of quiver gauge theories. https://doi.org/10.1088/1126-6708%2F2006%2F09%2F063

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