A deformed conifold with a cosmological constant

We find a new regular solution of six-dimensional Einstein's equations with a positive cosmological constant. It has the same isometry group as the (deformed) conifold geometry, and the superpotential approach is used to solve the equations of motion. The space is compact and interpolates between the deformed conifold and the resolved cone with a blown-up four cycle. The deformation/resolution parameters are set by the cosmological constant.Comment: 10 pages, 2 figures, JHEP style; v2: comments and references added, typos fixed; v3: even more comments addde

A Comment on Kerr-CFT and Wald Entropy

We point out that the entropies of black holes in general diffeomorphism invariant theories, computed using the Kerr-CFT correspondence and the Wald formula (as implemented in the entropy function formalism), need not always agree. A simple way to illustrate this is to consider Einstein-Gauss-Bonnet gravity in four dimensions, where the Gauss-Bonnet term is topological. This means that the central charge of Kerr-CFT computed in the Barnich-Brandt-Compere formalism remains the same as in Einstein gravity, while the entropy computed using the entropy function gives a universal correction proportional to the Gauss-Bonnet coupling. We argue that at least in this example, the Kerr-CFT result is the physically reasonable one. The resolution to this discrepancy might lie in a better understanding of boundary terms.Comment: 11 pages, v2,3: refs added, minor change

Brane polarization is no cure for tachyons

Anti-M2 and anti-D3 branes placed in regions with charges dissolved in fluxes have a tachyon in their near-horizon region, which causes these branes to repel each other. If the branes are on the Coulomb branch this tachyon gives rise to a runaway behavior, but when the branes are polarized into five-branes this tachyon only appears to lower the energy of the polarized branes, without affecting its stability. We analyze brane polarization in the presence of a brane-brane-repelling tachyon and show that when the branes are polarized along the direction of the tachyon the polarized shell is unstable. This implies that tachyons cannot be cured by brane polarization and indicates that, at least in a certain regime of parameters, anti-D3 branes polarized into NS5 branes at the bottom of the Klebanov-Strassler solution have an instability.Comment: 10 pages, 1 figure, JHEP styl

Spacetime emergence via holographic RG flow from incompressible Navier-Stokes at the horizon

We show that holographic RG flow can be defined precisely such that it corresponds to emergence of spacetime. We consider the case of pure Einstein's gravity with a negative cosmological constant in the dual hydrodynamic regime. The holographic RG flow is a system of first order differential equations for radial evolution of the energy-momentum tensor and the variables which parametrize it's phenomenological form on hypersurfaces in a foliation. The RG flow can be constructed without explicit knowledge of the bulk metric provided the hypersurface foliation is of a special kind. The bulk metric can be reconstructed once the RG flow equations are solved. We show that the full spacetime can be determined from the RG flow by requiring that the horizon fluid is a fixed point in a certain scaling limit leading to the non-relativistic incompressible Navier-Stokes dynamics. This restricts the near-horizon forms of all transport coefficients, which are thus determined independently of their asymptotic values and the RG flow can be solved uniquely. We are therefore able to recover the known boundary values of almost all transport coefficients at the first and second orders in the derivative expansion. We conjecture that the complete characterisation of the general holographic RG flow, including the choice of counterterms, might be determined from the hydrodynamic regime.Comment: 61 pages, 2 figures, 5 tables; matches with JHEP versio

Trivializing and Orbifolding the Conifold's Base

The conifold is a cone over the space T^11, which is known to be topologically S^2xS^3. The coordinates used in the literature describe a sphere-bundle which can be proven to be topologically trivializable. We provide an explicit trivialization of this bundle, with simultaneous global coordinates for both spheres. Using this trivialization we are able to describe the topology of the base of several infinite families of chiral and non-chiral orbifolds of the conifold. We demonstrate that in each case the 2nd Betti number of the base matches the number of independent ranks in the dual quiver gauge theory.Comment: 13 pages, 3 figure

Which BPS Baryons Minimize Volume?

A BPS 3-cycle in a Sasaki-Einstein 5-manifold in general does not minimize volume in its homology class, as we illustrate with several examples of non-minimal volume BPS cycles on the 5-manifolds Y(p,q). Instead they minimize the energy of a wrapping D-brane, extremizing a generalized calibration. We present this generalized calibration and demonstrate that it reproduces both the Born-Infeld and the Wess-Zumino parts of the D3-brane energy.Comment: 20 pages, 1 figure; citation added, references correcte

Polchinski-Strassler does not uplift Klebanov-Strassler

Anti-D3-branes at the tip of the Klebanov-Strassler solution with D3-charge dissolved in fluxes give rise, in the probe approximation, to a metastable state. The fully back-reacted smeared solution has singular three-form fluxes in the IR, whose presence suggests a stringy resolution by brane polarization a la Polchinski-Strassler. In this paper we show that there is no polarization into anti-D5-branes wrapping the $S^2$ of the conifold at a finite radius. The singularities therefore do not seem to be physical, signaling that antibranes cannot be used to uplift AdS and obtain a very large landscape of de Sitter vacua in string theory.Comment: 30 pages, 2 figures, JHEP style; v2: typos corrected, references added; v3: comments added and sign typo correcte

The Mesonic Branch of the Deformed Conifold

Using coordinates that manifest the S^2-S^3 split of the base, we study D3-branes localized on the three-sphere in the Klebanov-Strassler background. We find a numerical solution for the warp factor and show the emergence of the AdS throat near the stack. In the dual gauge theory, this corresponds to an RG flow along the mesonic branch. We demonstrate how the cubic superpotential of the N=4 SYM theory emerges at the end of the RG flow.Comment: 21 pages, 2 eps figures, v2: minor changes and corrections, references added, v3: JHEP versio