The Holographic Weyl anomaly

We calculate the Weyl anomaly for conformal field theories that can be described via the adS/CFT correspondence. This entails regularizing the gravitational part of the corresponding supergravity action in a manner consistent with general covariance. Up to a constant, the anomaly only depends on the dimension d of the manifold on which the conformal field theory is defined. We present concrete expressions for the anomaly in the physically relevant cases d = 2, 4 and 6. In d = 2 we find for the central charge c = 3 l/ 2 G_N in agreement with considerations based on the asymptotic symmetry algebra of adS_3. In d = 4 the anomaly agrees precisely with that of the corresponding N = 4 superconformal SU(N) gauge theory. The result in d = 6 provides new information for the (0, 2) theory, since its Weyl anomaly has not been computed previously. The anomaly in this case grows as N^3, where N is the number of coincident M5 branes, and it vanishes for a Ricci-flat background.Comment: 12 pages, Latex, v2: minor improvement

Non-equilibrium dynamics and AdS4AdS_4 Robinson-Trautman

The Robinson-Trautman space-times provide solutions of Einstein's equations with negative cosmological constant, which settle to $AdS_4$ Schwarzschild black hole at late times. Via gauge/gravity duality they should describe a system out of equilibrium that evolves towards thermalization. We show that the area of the past apparent horizon of these space-times satisfies a generalized Penrose inequality and we formulate as well as provide evidence for a suitable generalization of Thorne's hoop conjecture. We also compute the holographic energy-momentum tensor and deduce its late time behavior. It turns out that the complete non-equilibrium process on the boundary is governed by Calabi's flow on $S^2$. Upon linearization, only special modes that arise as supersymmetric zero energy states of an associated supersymmetric quantum mechanics problem contribute to the solution. We find that each pole of radiation has an effective viscosity given by the eigenvalues of the Laplace operator on $S^2$ and there is an apparent violation of the KSS bound on $\eta / s$ for the low lying harmonics of large $AdS_4$ black holes. These modes, however, do not satisfy Dirichlet boundary conditions, they are out-going and they do not appear to have a Kruskal extension across the future horizon ${\cal H}^+$.Comment: 48 pages, 2 figures, v2: new section on entropy current, refs added, JHEP versio

Weyl anomaly for Wilson surfaces

We consider a free two-form in six dimensions and calculate the conformal anomaly associated with a Wilson surface observable.Comment: 8 page

Robinson-Trautman spacetimes and gauge/gravity duality

We study far-from-equilibrium field theory dynamics using gauge/gravity duality applied to the Robinson-Trautman (RT) class of spacetimes and we present a number of new results. First, we assess the applicability of the hydrodynamic approximation to inhomogeneous plasma dynamics dual to RT spacetimes. We prove that to any order in a late time expansion it is possible to identify variables corresponding to the local energy density and fluid velocity. However, we show using numerical examples that this does not hold at the non-perturbative level; for sufficiently inhomogeneous initial data a local rest frame does not exist. Second, we preset a new class of holographic inhomogeneous plasma flows on the plane. The corresponding spacetimes are not of the RT type but they can be obtained from RT spacetimes with spatially compact boundaries by coordinate transformations which generate Poincar\'e patch-like coordinates with planar boundaries. We demonstrate the application of this procedure using numerical examples.Comment: Proceedings prepared for the "Workshop on Geometry and Physics" in memoriam of Ioannis Bakas, November 2016, Ringberg Castle, Germany. v2: Minor changes, added discussion of isotropisation tim

Observational signatures of holographic models of inflation

We discuss the phenomenology of recently proposed holographic models of inflation, in which the very early universe is non-geometric and is described by a dual three-dimensional quantum field theory (QFT). We analyze models determined by a specific class of dual QFTs and show that they have the following universal properties: (i) they have a nearly scale invariant spectrum of small amplitude primordial fluctuations, (ii) the scalar spectral index runs as alpha_s = -(n_s-1), (iii) the three-point function of primordial scalar perturbations is of exactly the factorizable equilateral form with f_nl^eq=5/36. These properties hold irrespective of the details (e.g. field content, strength of interactions, etc.) of the dual QFT within the class of theories we analyze. The ratio of tensors-to-scalars is determined by the field content of the dual QFT and does not satisfy the slow-roll consistency relations. Observations from the Planck satellite should be able to confirm or exclude these models.Comment: 4 pp, 2 fig

Open strings in the plane wave background II: Superalgebras and Spectra

In hep-th/0211011 we started a systematic investigation of open strings in the plane wave background. In this paper we continue the analysis by discussing the superalgebras of conserved charges, the spectra of open strings, and the spectra of DBI fluctuations around D-brane embeddings. We also derive the gluing conditions for corresponding boundary states and analyze their symmetries. All results are consistent with each other, and confirm the existence of additional supersymmetries as previously discussed. We further show that for every symmetry current one can construct a (countably) infinite number of related currents that contain more worldsheet derivatives, and discuss non-local symmetries.Comment: 48 page

Holography for Cosmology

We propose a holographic description of four-dimensional single-scalar inflationary universes, and show how cosmological observables, such as the primordial power spectrum, are encoded in the correlation functions of a three-dimensional QFT. The holographic description correctly reproduces standard inflationary predictions in the limit where a perturbative quantization of fluctuations is justified. In the opposite limit, wherein gravity is strongly coupled at early times, we propose a holographic description in terms of perturbative large N QFT. Initiating a holographic phenomenological approach, we show that models containing only two parameters, N and a dimensionful coupling constant, are capable of satisfying the current observational constraints.Comment: 5 pages; new figure displaying predicted spectral running

Correlation Functions in Holographic RG Flows

We discuss the computation of correlation functions in holographic RG flows. The method utilizes a recently developed Hamiltonian version of holographic renormalization and it is more efficient than previous methods. A significant simplification concerns the treatment of infinities: instead of performing a general analysis of counterterms, we develop a method where only the contribution of counterterms to any given correlator needs to be computed. For instance, the computation of renormalized 2-point functions requires only an analysis at the linearized level. We illustrate the method by discussing flat and AdS-sliced domain walls. In particular, we discuss correlation functions of the Janus solution, a recently discovered non-supersymmetric but stable AdS-sliced domain wall.Comment: 33 pages, v2 additional material on Janus solution, typos corrected, refs added, v3 additional comments on Janus solution, figure added, version to appear in JHE