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We construct supergravity solutions describing a stack of D3-branes localized at a point on a blown-up cycle of a resolved La,b,c cone. The geometry flows from AdS5 × La,b,c to AdS5 × S5 × Zk. The corresponding quiver gauge theory undergoes a renormalization group flow between two superconformal fixed points, which leads to semi-infinite chains of flows between the various La;b;c fixed points. The general system is described by a triplet of Heun equations, which can each be solved by an expansion with a three-term recursion relation, though there are closed-form solutions for certain cases. This enables us to read off the operators that acquire nonzero vacuum expectation values as the quiver gauge theory flows away from a fixed point.
Date Posted: 25 January 2011
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