Conformal gravity holography in four dimensions

We formulate four-dimensional conformal gravity with (Anti-)de Sitter boundary conditions that are weaker than Starobinsky boundary conditions, allowing for an asymptotically subleading Rindler term concurrent with a recent model for gravity at large distances. We prove the consistency of the variational principle and derive the holographic response functions. One of them is the conformal gravity version of the Brown-York stress tensor, the other is a `partially massless response'. The on-shell action and response functions are finite and do not require holographic renormalization. Finally, we discuss phenomenologically interesting examples, including the most general spherically symmetric solutions and rotating black hole solutions with partially massless hair.Comment: 5pp; v2: Minor clarifications and edits, added references. Phys. Rev. Lett. versio

The Interplay Between θ\theta and T

We extend a recent computation of the dependence of the free energy, F, on the noncommutative scale $\theta$ to theories with very different UV sensitivity. The temperature dependence of $F$ strongly suggests that a reduced number of degrees of freedom contributes to the free energy in the non-planar sector, $F_{\rm np}$, at high temperature. This phenomenon seems generic, independent of the UV sensitivity, and can be traced to modes whose thermal wavelengths become smaller than the noncommutativity scale. The temperature dependence of $F_{\rm np}$ can then be calculated at high temperature using classical statistical mechanics, without encountering a UV catastrophe even in large number of dimensions. This result is a telltale sign of the low number of degrees of freedom contributing to $F$ in the non-planar sector at high temperature. Such behavior is in marked contrast to what would happen in a field theory with a random set of higher derivative interactions.Comment: 14 pages, 1 eps figur

Hamilton-Jacobi Counterterms for Einstein-Gauss-Bonnet Gravity

The on-shell gravitational action and the boundary stress tensor are essential ingredients in the study of black hole thermodynamics. We employ the Hamilton-Jacobi method to calculate the boundary counterterms necessary to remove the divergences and allow the study of the thermodynamics of Einstein-Gauss-Bonnet black holes.Comment: 21 pages, LaTe

N-body Gravity and the Schroedinger Equation

We consider the problem of the motion of $N$ bodies in a self-gravitating system in two spacetime dimensions. We point out that this system can be mapped onto the quantum-mechanical problem of an N-body generalization of the problem of the H$_{2}^{+}$ molecular ion in one dimension. The canonical gravitational N-body formalism can be extended to include electromagnetic charges. We derive a general algorithm for solving this problem, and show how it reduces to known results for the 2-body and 3-body systems.Comment: 15 pages, Latex, references added, typos corrected, final version that appears in CQ

Thermodynamics of Black Holes in Two (and Higher) Dimensions

A comprehensive treatment of black hole thermodynamics in two-dimensional dilaton gravity is presented. We derive an improved action for these theories and construct the Euclidean path integral. An essentially unique boundary counterterm renders the improved action finite on-shell, and its variational properties guarantee that the path integral has a well-defined semi-classical limit. We give a detailed discussion of the canonical ensemble described by the Euclidean partition function, and examine various issues related to stability. Numerous examples are provided, including black hole backgrounds that appear in two dimensional solutions of string theory. We show that the Exact String Black Hole is one of the rare cases that admits a consistent thermodynamics without the need for an external thermal reservoir. Our approach can also be applied to certain higher-dimensional black holes, such as Schwarzschild-AdS, Reissner-Nordstrom, and BTZ.Comment: 63 pages, 3 pdf figures, v2: added reference

Winding effects on brane/anti-brane pairs

We study a brane/anti-brane configuration which is separated along a compact direction by constructing a tachyon effective action which takes into account transverse scalars. Such an action is relevant in the study of HQCD model of Sakai and Sugimoto of chiral symmetry breaking, where the size of the compact circle sets the confinement scale. Our approach is motivated by string theory orbifold constructions and gives a route to model inhomogeneous tachyon decay. We illustrate the techniques involved with a relatively simple example of a harmonic oscillator on a circle. We will then repeat the analysis for the Sakai-Sugimoto model and show that by integrating out the winding modes will provide us with a renormalized action with a lower energy than that of truncating to zero winding sector.Comment: 21 pages, 3 figures. v3: discussion and references added, published versio

UV-divergences of Wilson Loops for Gauge/Gravity Duality

We analyze the structure of the UV divergences of the Wilson loop for a general gauge/gravity duality. We find that, due to the presence of a nontrivial NSNS B-field and metric, new divergences that cannot be subtracted out by the conventional Legendre transform may arise. We also derive conditions on the B-field and the metric, which when satisfied, the leading UV divergence will become linear, and can be cancelled out by choosing the boundary condition of the string appropriately. Our results, together with the recent result of arXiv:0807.5127, where the effect of a nontrivial dilaton on the structure of UV divergences in Wilson loop is analysed, allow us to conclude that Legendre transform is at best capable of cancelling the linear UV divergences arising from the area of the worldsheet, but is incapable to handle the divergences associated with the dilaton or the B-field in general. We also solve the conditions for the cancellation of the leading linear divergences generally and find that many well-known supergravity backgrounds are of these kinds, including examples such as the Sakai-Sugimoto QCD model or N=1 duality with Sasaki-Einstein spaces. We also point out that Wilson loop in the Klebanov-Strassler background have a divergence associated with the B-field which cannot be cancelled away with the Legendre transform. Finally we end with some comments on the form of the Wilson loop operator in the ABJM superconformal Chern-Simons theory.Comment: 26 pages. LaTeX. v2: reference added. version to appear in JHE

Entropy of the Stiffest Stars

We analyze the properties of stars whose interior is described by the stiffest equation of state consistent with causality. We note the remarkable fact that the entropy of such stars scales like the area.Comment: 16 pages, 5 figure

String theory duals of Lifshitz-Chern-Simons gauge theories

We propose candidate gravity duals for a class of non-Abelian z=2 Lifshitz Chern-Simons (LCS) gauge theories studied by Mulligan, Kachru and Nayak. These are nonrelativistic gauge theories in 2+1 dimensions in which parity and time-reversal symmetries are explicitly broken by the presence of a Chern-Simons term. We show that these field theories can be realized as deformations of DLCQ N=4 super Yang-Mills theory. Using the holographic dictionary, we identify the bulk fields that are dual to these deformations. The geometries describing the groundstates of the non-Abelian LCS gauge theories realized here exhibit a mass gap.Comment: 25+14 pages, 3 figures; v2: significant corrections regarding IR geometry, resulting in new section 5; journal versio

Correlation Functions of Operators and Wilson Surfaces in the d=6, (0,2) Theory in the Large N Limit

We compute the two and three-point correlation functions of chiral primary operators in the large N limit of the (0,2), d=6 superconformal theory. We also consider the operator product expansion of Wilson surfaces in the (0,2) theory and compute the OPE coefficients of the chiral primary operators at large N from the correlation functions of surfaces.Comment: 34 pages, using utarticle.cls (included), array.sty, amsmath.sty, amsfonts.sty, latexsym.sty, epsfig. Bibtex style: utphys.bst (.bbl file included