Warped Resolved L^{a,b,c} Cones

TL;DR

This paper constructs supergravity solutions for D3-branes on resolved L^{a,b,c} cones, revealing RG flows between superconformal fixed points and providing insights into the dual quiver gauge theories.

Contribution

It introduces explicit supergravity solutions describing D3-branes on resolved L^{a,b,c} cones and analyzes the resulting RG flows and operator VEVs in the dual gauge theories.

Findings

Flow from AdS_5 x L^{a,b,c} to AdS_5 x S^5/Z_k

Solutions involve Heun equations with recursive expansions

Identification of operators with non-zero VEVs during flows

Abstract

We construct supergravity solutions describing a stack of D3-branes localized at a point on a blown-up cycle of a resolved L^{a,b,c} cone. The geometry flows from AdS_5 x L^{a,b,c} to AdS_5 x S^5/Z_k. The corresponding quiver gauge theory undergoes an RG flow between two superconformal fixed points, which leads to semi-infinite chains of flows between the various L^{a,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 which acquire non-zero vacuum expectation values as the quiver gauge theory flows away from a fixed point.