Gravity in the 3+1-Split Formalism II: Self-Duality and the Emergence of the Gravitational Chern-Simons in the Boundary

We study self-duality in the context of the 3+1-split formalism of gravity with non-zero cosmological constant. Lorentzian self-dual configurations are conformally flat spacetimes and have boundary data determined by classical solutions of the three-dimensional gravitational Chern-Simons. For Euclidean self-dual configurations, the relationship between their boundary initial positions and initial velocity is also determined by the three-dimensional gravitational Chern-Simons. Our results imply that bulk self-dual configurations are holographically described by the gravitational Chern-Simons theory which can either viewed as a boundary generating functional or as a boundary effective action.Comment: 25 pages; v2: minor improvements, references adde

Generalized Holographic Cosmology

We consider general black hole solutions in five-dimensional spacetime in the presence of a negative cosmological constant. We obtain a cosmological evolution via the gravity/gauge theory duality (holography) by defining appropriate boundary conditions on a four-dimensional boundary hypersurface. The standard counterterms are shown to renormalize the bare parameters of the system (the four-dimensional Newton's constant and cosmological constant). We discuss the thermodynamics of cosmological evolution and present various examples. The standard brane-world scenarios are shown to be special cases of our holographic construction.Comment: 15 pages, 5 figure

Gravity in the 3+1-Split Formalism I: Holography as an Initial Value Problem

We present a detailed analysis of the 3+1-split formalism of gravity in the presence of a cosmological constant. The formalism helps revealing the intimate connection between holography and the initial value formulation of gravity. We show that the various methods of holographic subtraction of divergences correspond just to different transformations of the canonical variables, such that the initial value problem is properly set up at the boundary. The renormalized boundary energy momentum tensor is a component of the Weyl tensor.Comment: 28 pages; v2: minor improvements, references adde

Remarks on Resonant Scalars in the AdS/CFT Correspondence

The special properties of scalars having a mass such that the two possible dimensions of the dual scalar respect the unitarity and the Breitenlohner-Freedman bounds and their ratio is integral (``resonant scalars'') are studied in the AdS/CFT correspondence. The role of logarithmic branches in the gravity theory is related to the existence of a trace anomaly and to a marginal deformation in the Conformal Field Theory. The existence of asymptotic charges for the conformal group in the gravity theory is interpreted in terms of the properties of the corresponding CFT.Comment: 16 pages, 1 figur

A Field-theoretical Interpretation of the Holographic Renormalization Group

A quantum-field theoretical interpretation is given to the holographic RG equation by relating it to a field-theoretical local RG equation which determines how Weyl invariance is broken in a quantized field theory. Using this approach we determine the relation between the holographic C theorem and the C theorem in two-dimensional quantum field theory which relies on the Zamolodchikov metric. Similarly we discuss how in four dimensions the holographic C function is related to a conjectured field-theoretical C function. The scheme dependence of the holographic RG due to the possible presence of finite local counterterms is discussed in detail, as well as its implications for the holographic C function. We also discuss issues special to the situation when mass deformations are present. Furthermore we suggest that the holographic RG equation may also be obtained from a bulk diffeomorphism which reduces to a Weyl transformation on the boundary.Comment: 24 pages, LaTeX, no figures; references added, typos corrected, paragraph added to section

Irrelevant deformations and the holographic Callan-Symanzik equation

We discuss the systematics of obtaining the Callan-Symanzik equation within the framework of the gauge/gravity dualities. We present a completely general formula which in particular takes into account the new holographic renormalization results of arXiv:1102.2239. Non-trivial beta functions are obtained from new logarithmic terms in the radial expansion of the fields. The appearance of multi-trace counterterms is also discussed in detail and we show that mixing between single- and multi-trace operators leads to very specific non-linearities in the Callan-Symanzik equation. Additionally, we compute the conformal anomaly for a scalar three-point function in a CFT.Comment: 40 page

Some Calculable Contributions to Holographic Entanglement Entropy

Using the AdS/CFT correspondence, we examine entanglement entropy for a boundary theory deformed by a relevant operator and establish two results. The first is that if there is a contribution which is logarithmic in the UV cut-off, then the coefficient of this term is independent of the state of the boundary theory. In fact, the same is true of all of the coefficients of contributions which diverge as some power of the UV cut-off. Secondly, we show that the relevant deformation introduces new logarithmic contributions to the entanglement entropy. The form of some of these new contributions is similar to that found recently in an investigation of entanglement entropy in a free massive scalar field theory [1].Comment: 52 pages, no figure

Thermodynamics and Instabilities of a Strongly Coupled Anisotropic Plasma

We extend our analysis of a IIB supergravity solution dual to a spatially anisotropic finite-temperature N=4 super Yang-Mills plasma. The solution is static, possesses an anisotropic horizon, and is completely regular. The full geometry can be viewed as a renormalization group flow from an AdS geometry in the ultraviolet to a Lifshitz-like geometry in the infrared. The anisotropy can be equivalently understood as resulting from a position-dependent theta-term or from a non-zero number density of dissolved D7-branes. The holographic stress tensor is conserved and anisotropic. The presence of a conformal anomaly plays an important role in the thermodynamics. The phase diagram exhibits homogeneous and inhomogeneous (i.e. mixed) phases. In some regions the homogeneous phase displays instabilities reminiscent of those of weakly coupled plasmas. We comment on similarities with QCD at finite baryon density and with the phenomenon of cavitation.Comment: 62 pages, 13 figures; v2: typos fixed, added reference