Gauge/Gravity Duality and Warped Resolved Conifold

TL;DR

This paper constructs explicit supergravity solutions for warped conifolds in the gauge/string duality, revealing how different vacua correspond to smooth RG flows and baryonic condensates in the dual gauge theory.

Contribution

It provides explicit warped supergravity backgrounds for both singular and resolved conifolds, matching them with gauge theory vacua and analyzing baryonic condensates.

Findings

Constructed non-singular warped solutions for the resolved conifold.

Described RG flow from AdS_5×T^{1,1} to AdS_5×S^5.

Confirmed baryonic condensate via Euclidean D3-brane analysis.

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.