Gauge/Gravity Duality and Warped Resolved Conifold
Igor R. Klebanov, Arvind Murugan
TL;DR
The paper constructs explicit non-singular SUGRA duals for vacua of the ${\cal N}=1$ ${\rm SU}(N)\times{\rm SU}(N)$ theory on D3-branes at the conifold, including vacua with ${\cal U}\neq 0$ that map to D3-branes on the resolved conifold. It develops Green's-function techniques on the singular and resolved conifolds and matches normalizable supergravity fluctuations to gauge-theory operator VEVs of the bifundamentals $A_i,B_j$, revealing a holographic RG flow from $AdS_5\times T^{1,1}$ in the UV to $AdS_5\times S^5$ in the IR. For the resolved case, a stack localized on the blown-up $S^2$ yields a non-singular warped solution with unbroken $SU(2)\times U(1)\times U(1)$, dual to a baryonic branch where ${\rm det} B_2$ acquires a VEV; this is corroborated by a Euclidean D3-brane computation of the condensate. The work also analyzes turning on a fluxless NS-NS $B_2$ field to access generic gauge couplings, and discusses extensions to other Sasaki–Einstein geometries and potential applications to inflationary brane setups.
Abstract
We study supergravity backgrounds encoded through the gauge/string correspondence by the SU(N) \times SU(N) theory arising on N D3-branes on the conifold. As discussed in hep-th/9905104, the dynamics of this theory describes warped versions of both the singular and the resolved conifolds through different (symmetry breaking) vacua. We construct these supergravity solutions explicitly and match them with the gauge theory with different sets of vacuum expectation values of the bi-fundamental fields A_1, A_2, B_1, B_2. For the resolved conifold, we find a non-singular SU(2)\times U(1)\times U(1) symmetric warped solution produced by a stack of D3-branes localized at a point on the blown-up 2-sphere. It describes a smooth RG flow from AdS_5 \times T^{1,1} in the UV to AdS_5 \times S^5 in the IR, produced by giving a VEV to just one field, e.g. B_2. The presence of a condensate of baryonic operator det B_2 is confirmed using a Euclidean D3-brane wrapping a 4-cycle inside the resolved conifold. The Green's functions on the singular and resolved conifolds are central to our calculations and are discussed in some detail.