Conformal Field Theories in Fractional Dimensions

We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary CFTs connecting the 2D Ising model, the 3D Ising model, and the free scalar theory in 4D. We give numerical predictions for the leading operator dimensions and central charge in this family at different values of D and compare these to calculations of phi^4 theory in the epsilon-expansion.Comment: 11 pages, 4 figures - references updated - one affiliation modifie

Simplifying instanton corrections to N=4 SYM correlators

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Massive Gravity Theories and limits of Ghost-free Bigravity models

We construct a class of theories which extend New Massive Gravity to higher orders in curvature in any dimension. The lagrangians arise as limits of a new class of bimetric theories of Lovelock gravity, which are unitary theories free from the Boulware-Deser ghost. These Lovelock bigravity models represent the most general non-chiral ghost-free theories of an interacting massless and massive spin-two field in any dimension. The scaling limit is taken in such a way that unitarity is explicitly broken, but the Boulware-Deser ghost remains absent. This automatically implies the existence of a holographic $c$-theorem for these theories. We also show that the Born-Infeld extension of New Massive Gravity falls into our class of models demonstrating that this theory is also free of the Boulware-Deser ghost. These results extend existing connections between New Massive Gravity, bigravity theories, Galileon theories and holographic $c$-theorems.Comment: 11+5 page

Holographic studies of quasi-topological gravity

Quasi-topological gravity is a new gravitational theory including curvature-cubed interactions and for which exact black hole solutions were constructed. In a holographic framework, classical quasi-topological gravity can be thought to be dual to the large $N_c$ limit of some non-supersymmetric but conformal gauge theory. We establish various elements of the AdS/CFT dictionary for this duality. This allows us to infer physical constraints on the couplings in the gravitational theory. Further we use holography to investigate hydrodynamic aspects of the dual gauge theory. In particular, we find that the minimum value of the shear-viscosity-to-entropy-density ratio for this model is $\eta/s \simeq 0.4140/(4\pi)$.Comment: 45 pages, 6 figures. v2: References adde

Comments on Holographic Entanglement Entropy and RG Flows

Using holographic entanglement entropy for strip geometry, we construct a candidate for a c-function in arbitrary dimensions. For holographic theories dual to Einstein gravity, this c-function is shown to decrease monotonically along RG flows. A sufficient condition required for this monotonic flow is that the stress tensor of the matter fields driving the holographic RG flow must satisfy the null energy condition over the holographic surface used to calculate the entanglement entropy. In the case where the bulk theory is described by Gauss-Bonnet gravity, the latter condition alone is not sufficient to establish the monotonic flow of the c-function. We also observe that for certain holographic RG flows, the entanglement entropy undergoes a 'phase transition' as the size of the system grows and as a result, evolution of the c-function may exhibit a discontinuous drop.Comment: References adde

Short-cut to new anomalies in gravity duals to logarithmic conformal field theories

Various massive gravity theories in three dimensions are conjecturally dual to logarithmic conformal field theories (LCFTs). We summarise the status of these conjectures. LCFTs are characterised by the values of the central charges and the so-called "new anomalies". We employ a short-cut to calculate these new anomalies in generalised massive gravity and in the recently proposed higher-derivative gravity theories with holographic c-theorem. Both cases permit LCFTs exhibiting intriguing features, like rank three Jordan cells or non-zero central charges. Finally, as an example we discuss in some detail the partially massless version of new massive gravity, a theory with several special properties that we call "partially massless gravity".Comment: 34 pages, 2 figures; v2: added references; v3: Several rewordings in the introduction and section 2, added references. Matches published versio

Universality and exactness of Schrodinger geometries in string and M-theory

We propose an organizing principle for classifying and constructing Schrodinger-invariant solutions within string theory and M-theory, based on the idea that such solutions represent nonlinear completions of linearized vector and graviton Kaluza-Klein excitations of AdS compactifications. A crucial simplification, derived from the symmetry of AdS, is that the nonlinearities appear only quadratically. Accordingly, every AdS vacuum admits infinite families of Schrodinger deformations parameterized by the dynamical exponent z. We exhibit the ease of finding these solutions by presenting three new constructions: two from M5 branes, both wrapped and extended, and one from the D1-D5 (and S-dual F1-NS5) system. From the boundary perspective, perturbing a CFT by a null vector operator can lead to nonzero beta-functions for spin-2 operators; however, symmetry restricts them to be at most quadratic in couplings. This point of view also allows us to easily prove nonrenormalization theorems: for any Sch(z) solution of two-derivative supergravity constructed in the above manner, z is uncorrected to all orders in higher derivative corrections if the deforming KK mode lies in a short multiplet of an AdS supergroup. Furthermore, we find infinite classes of 1/4 BPS solutions with 4-,5- and 7-dimensional Schrodinger symmetry that are exact.Comment: 31 pages, plus appendices; v2, minor corrections, added refs, slight change in interpretation in section 2.3, new Schrodinger and Lifshitz solutions included; v3, clarifications in sections 2 and 3 regarding existence of solutions and multi-trace operator

Holographic GB gravity in arbitrary dimensions

We study the properties of the holographic CFT dual to Gauss-Bonnet gravity in general $D \ge 5$ dimensions. We establish the AdS/CFT dictionary and in particular relate the couplings of the gravitational theory to the universal couplings arising in correlators of the stress tensor of the dual CFT. This allows us to examine constraints on the gravitational couplings by demanding consistency of the CFT. In particular, one can demand positive energy fluxes in scattering processes or the causal propagation of fluctuations. We also examine the holographic hydrodynamics, commenting on the shear viscosity as well as the relaxation time. The latter allows us to consider causality constraints arising from the second-order truncated theory of hydrodynamics.Comment: 48 pages, 9 figures. v2: New discussion on free fields in subsection 3.3 and new appendix B on conformal tensor fields. Added comments on the relation between the central charge appearing in the two-point function and the "central charge" characterizing the entropy density in the discussion. References adde

A Lovelock black hole bestiary

We revisit the study of (A)dS black holes in Lovelock theories. We present a new tool that allows to attack this problem in full generality. In analyzing maximally symmetric Lovelock black holes with non-planar horizon topologies many distinctive and interesting features are observed. Among them, the existence of maximally symmetric vacua do not supporting black holes in vast regions of the space of gravitational couplings, multi-horizon black holes, and branches of solutions that suggest the existence of a rich diagram of phase transitions. The appearance of naked singularities seems unavoidable in some cases, raising the question about the fate of the cosmic censorship conjecture in these theories. There is a preferred branch of solutions for planar black holes, as well as non-planar black holes with high enough mass or temperature. Our study clarifies the role of all branches of solutions, including asymptotically dS black holes, and whether they should be considered when studying these theories in the context of AdS/CFT.Comment: 40 pages, 16 figures; v2: references added and minor amendments; v3: title changed to improve its accuracy and general reorganization of the results to ameliorate their presentatio

Moduli and electromagnetic black brane holography

We investigate the thermodynamic and hydrodynamic properties of 4-dimensional gauge theories with finite electric charge density in the presence of a constant magnetic field. Their gravity duals are planar magnetically and electrically charged AdS black holes in theories that contain a gauge Chern-Simons term. We present a careful analysis of the near horizon geometry of these black branes at finite and zero temperature for the case of a scalar field non-minimally coupled to the electromagnetic field. With the knowledge of the near horizon data, we obtain analytic expressions for the shear viscosity coefficient and entropy density, and also study the effect of a generic set of four derivative interactions on their ratio. We also comment on the attractor flows of the extremal solutions.Comment: 39 pages, no figures; v2: minor changes, refs. added; v3: typo fixed; v4: a proof for decoupling of the viscosity mode added in appendix, matches the published versio