Anatomy of bubbling solutions

We present a comprehensive analysis of holography for the bubbling solutions of Lin-Lunin-Maldacena. These solutions are uniquely determined by a coloring of a 2-plane, which was argued to correspond to the phase space of free fermions. We show that in general this phase space distribution does not determine fully the 1/2 BPS state of N=4 SYM that the gravitational solution is dual to, but it does determine it enough so that vevs of all single trace 1/2 BPS operators in that state are uniquely determined to leading order in the large N limit. These are precisely the vevs encoded in the asymptotics of the LLM solutions. We extract these vevs for operators up to dimension 4 using holographic renormalization and KK holography and show exact agreement with the field theory expressions.Comment: 67 pages, 6 figures; v2: typos corrected, refs added; v3: expanded explanations, more typos correcte

Dressed spectral densities for heavy quark diffusion in holographic plasmas

We analyze the large frequency behavior of the spectral densities that govern the generalized Langevin diffusion process for a heavy quark in the context of the gauge/gravity duality. The bare Langevin correlators obtained from the trailing string solution have a singular short-distance behavior. We argue that the proper dressed spectral functions are obtained by subtracting the zero-temperature correlators. The dressed spectral functions have a sufficiently fast fall-off at large frequency so that the Langevin process is well defined and the dispersion relations are satisfied. We identify the cases in which the subtraction does not modify the associated low-frequency transport coefficients. These include conformal theories and the non-conformal, non-confining models. We provide several analytic and numerical examples in conformal and non-conformal holographic backgrounds.Comment: 51 pages, 2 figure

On the existence of supergravity duals to D1--D5 CFT states

We define a metric operator in the 1/2-BPS sector of the D1-D5 CFT, the eigenstates of which have a good semi-classical supergravity dual; the non-eigenstates cannot be mapped to semi-classical gravity duals. We also analyse how the data defining a CFT state manifests itself in the gravity side, and show that it is arranged into a set of multipoles. Interestingly, we find that quantum mechanical interference in the CFT can have observable manifestations in the semi-classical gravity dual. We also point out that the multipoles associated to the normal statistical ensemble fluctuate wildly, indicating that the mixed thermal state should not be associated to a semi-classical geometry.Comment: 22 pages, 2 figures. v2 : references added, typos correcte

A consistent truncation of IIB supergravity on manifolds admitting a Sasaki-Einstein structure

We present a consistent truncation of IIB supergravity on manifolds admitting a Sasaki-Einstein structure, which keeps the metric and five real scalar fields. This theory can be further truncated to a constrained one-parameter family that depends on only the metric and one scalar, as well as to a theory with a metric and three scalars. The reduced theory admits supersymmetric and non-supersymmetric AdS_5 and AdS_4 x R solutions. We analyze the spectrum around the AdS critical points and identify the dual operators.Comment: 21 pages; v2: references added and minor improvement

Holographic Renormalization for z=2 Lifshitz Space-Times from AdS

Lifshitz space-times with critical exponent z=2 can be obtained by dimensional reduction of Schroedinger space-times with critical exponent z=0. The latter space-times are asymptotically AdS solutions of AdS gravity coupled to an axion-dilaton system and can be uplifted to solutions of type IIB supergravity. This basic observation is used to perform holographic renormalization for 4-dimensional asymptotically z=2 locally Lifshitz space-times by Scherk-Schwarz dimensional reduction of the corresponding problem of holographic renormalization for 5-dimensional asymptotically locally AdS space-times coupled to an axion-dilaton system. We can thus define and characterize a 4-dimensional asymptotically locally z=2 Lifshitz space-time in terms of 5-dimensional AdS boundary data. In this setup the 4-dimensional structure of the Fefferman-Graham expansion and the structure of the counterterm action, including the scale anomaly, will be discussed. We find that for asymptotically locally z=2 Lifshitz space-times obtained in this way there are two anomalies each with their own associated nonzero central charge. Both anomalies follow from the Scherk--Schwarz dimensional reduction of the 5-dimensional conformal anomaly of AdS gravity coupled to an axion-dilaton system. Together they make up an action that is of the Horava-Lifshitz type with nonzero potential term for z=2 conformal gravity.Comment: 32 pages, v2: modified discussion of the central charge

Fake supersymmetry versus Hamilton-Jacobi

We explain when the first-order Hamilton-Jacobi equations for black holes (and domain walls) in (gauged) supergravity, reduce to the usual first-order equations derived from a fake superpotential. This turns out to be equivalent to the vanishing of a newly found constant of motion and we illustrate this with various examples. We show that fake supersymmetry is a necessary condition for having physically sensible extremal black hole solutions. We furthermore observe that small black holes become scaling solutions near the horizon. When combined with fake supersymmetry, this leads to a precise extension of the attractor mechanism to small black holes: The attractor solution is such that the scalars move on specific curves, determined by the black hole charges, that are purely geodesic, although there is a non-zero potential.Comment: 20 pages, v2: Typos corrected, references adde

Relativistic Viscous Fluid Dynamics and Non-Equilibrium Entropy

Fluid dynamics corresponds to the dynamics of a substance in the long wavelength limit. Writing down all terms in a gradient (long wavelength) expansion up to second order for a relativistic system at vanishing charge density, one obtains the most general (causal) equations of motion for a fluid in the presence of shear and bulk viscosity, as well as the structure of the non-equilibrium entropy current. Requiring positivity of the divergence of the non-equilibrium entropy current relates some of its coefficients to those entering the equations of motion. I comment on possible applications of these results for conformal and non-conformal fluids.Comment: 25 pages, no figures; v2: matches published versio

Finite-Temperature Fractional D2-Branes and the Deconfinement Transition in 2+1 Dimensions

The supergravity dual to N regular and M fractional D2-branes on the cone over \mathbb{CP}^3 has a naked singularity in the infrared. One can resolve this singularity and obtain a regular fractional D2-brane solution dual to a confining 2+1 dimensional N = 1 supersymmetric field theory. The confining vacuum of this theory is described by the solution of Cvetic, Gibbons, Lu and Pope. In this paper, we explore the alternative possibility for resolving the singularity - the creation of a regular horizon. The black-hole solution we find corresponds to the deconfined phase of this dual gauge theory in three dimensions. This solution is derived in perturbation theory in the number of fractional branes. We argue that there is a first-order deconfinement transition. Connections to Chern--Simons matter theories, the ABJM proposal and fractional M2-branes are presented.Comment: v3: analytic solutions are expose

Domain walls in three dimensional gauged supergravity

We explicitly construct two Chern-Simons gauged supergravities in three dimensions with N=4 and N=8 supersymmetries and non-semisimple gauge groups. The N=4 theory has scalar manifold $SO(4,3)/SO(4)\times SO(3)$ with the gauge group $SO(3)\ltimes (\mathbf{T}^3,\hat{\mathbf{T}}^3)$. The theory describes (1,0) six dimensional supergravity reduced on an SU(2) group manifold. The equivalent Yang-Mills type gauged supergravity has SO(3) gauge group coupled to three massive vector fields. The N=8 theory is described by $SO(8,8)/SO(8)\times SO(8)$ scalar manifold, and the gauge group is given by $SO(8)\ltimes \mathbf{T}^{28}$. The theory is a truncation of the $SO(8)\ltimes \mathbf{T}^{28}$ gauged N=16 theory with scalar manifold $E_{8(8)}/SO(16)$ and can be obtained by an S^7 compactification of type I theory in ten dimensions. Domain wall solutions of both gauged supergravities are analytically found and can be uplifted to higher dimensions. These provide domain wall vacua in the three dimensional gauged supergravity framework which might be useful for the study of Domain Wall$_3$/QFT$_2$ correspondence.Comment: 19 pages, no figures, typoes and a mistake in a sign corrected, clarifications on the notations adde

Non-conformal Hydrodynamics in Einstein-dilaton Theory

In the Einestein-dilaton theory with a Liouville potential parameterized by $\eta$, we find a Schwarzschild-type black hole solution. This black hole solution, whose asymptotic geometry is described by the warped metric, is thermodynamically stable only for $0 \le \eta < 2$. Applying the gauge/gravity duality, we find that the dual gauge theory represents a non-conformal thermal system with the equation of state depending on $\eta$. After turning on the bulk vector fluctuations with and without a dilaton coupling, we calculate the charge diffusion constant, which indicates that the life time of the quasi normal mode decreases with $\eta$. Interestingly, the vector fluctuation with the dilaton coupling shows that the DC conductivity increases with temperature, a feature commonly found in electrolytes.Comment: 27 pages and 2 figures, published in JHE