Symmetry-breaking and zero-one laws

We offer further evidence that discreteness of the sort inherent in a causal set cannot, in and of itself, serve to break Poincaré invariance. In particular we prove that a Poisson sprinkling of Minkowski spacetime cannot endow spacetime with a distinguished spatial or temporal orientation, or with a distinguished lattice of spacetime points, or with a distinguished lattice of timelike directions (corresponding respectively to breakings of reflection-invariance, translation-invariance, and Lorentz invariance). Along the way we provide a proof from first principles of the zero-one law on which our new arguments are based

A Distinguished Vacuum State for a Quantum Field in a Curved Spacetime: Formalism, Features, and Cosmology

We define a distinguished "ground state" or "vacuum" for a free scalar quantum field in a globally hyperbolic region of an arbitrarily curved spacetime. Our prescription is motivated by the recent construction of a quantum field theory on a background causal set using only knowledge of the retarded Green's function. We generalize that construction to continuum spacetimes and find that it yields a distinguished vacuum or ground state for a non-interacting, massive or massless scalar field. This state is defined for all compact regions and for many noncompact ones. In a static spacetime we find that our vacuum coincides with the usual ground state. We determine it also for a radiation-filled, spatially homogeneous and isotropic cosmos, and show that the super-horizon correlations are approximately the same as those of a thermal state. Finally, we illustrate the inherent non-locality of our prescription with the example of a spacetime which sandwiches a region with curvature in-between flat initial and final regions

Stable non-uniform black strings below the critical dimension

The higher-dimensional vacuum Einstein equation admits translationally non-uniform black string solutions. It has been argued that infinitesimally non-uniform black strings should be unstable in 13 or fewer dimensions and otherwise stable. We construct numerically non-uniform black string solutions in 11, 12, 13, 14 and 15 dimensions. Their stability is investigated using local Penrose inequalities. Weakly non-uniform solutions behave as expected. However, in 12 and 13 dimensions, strongly non-uniform solutions appear to be stable and can have greater horizon area than a uniform string of the same mass. In 14 and 15 dimensions all non-uniform black strings appear to be stable.Comment: 26 pages, 11 figures. V2: reference added, matches published versio

Bounds for State Degeneracies in 2D Conformal Field Theory

In this note we explore the application of modular invariance in 2-dimensional CFT to derive universal bounds for quantities describing certain state degeneracies, such as the thermodynamic entropy, or the number of marginal operators. We show that the entropy at inverse temperature 2 pi satisfies a universal lower bound, and we enumerate the principal obstacles to deriving upper bounds on entropies or quantum mechanical degeneracies for fully general CFTs. We then restrict our attention to infrared stable CFT with moderately low central charge, in addition to the usual assumptions of modular invariance, unitarity and discrete operator spectrum. For CFT in the range c_left + c_right < 48 with no relevant operators, we are able to prove an upper bound on the thermodynamic entropy at inverse temperature 2 pi. Under the same conditions we also prove that a CFT can have a number of marginal deformations no greater than ((c_left + c_right) / (48 - c_left - c_right)) e^(4 Pi) - 2.Comment: 23 pages, LaTeX, minor change

A regularisation approach to causality theory for C^{1,1}Lorentzian metrics

We show that many standard results of Lorentzian causality theory remain valid if the regularity of the metric is reduced to C^{1,1}. Our approach is based on regularisations of the metric adapted to the causal structure

KK6 from M2 in BLG

We study the possibility that the Kaluza-Klein monopole (KK6) world-volume action may be obtained from the multiple membranes (M2) action which is described by BLG theory. We first point out that the infinite dimensional Lie 3-algebra based on the Nambu-Poisson structure could not only provide three dimensional manifolds to allow M5 from M2, which was studied by previous authors, but also provide five dimensional manifolds to allow KK6 from M2. We next present a possible way that the U(1) field on KK6 world-volume action could be produced form the gauge potential in BLG theory.Comment: Latex, 15 pages. V3: Add theorem 2 to complete proof. V4: Detail physical interpretations and calculations in section

Entropy bounds in terms of the w parameter

In a pair of recent articles [PRL 105 (2010) 041302 - arXiv:1005.1132; JHEP 1103 (2011) 056 - arXiv:1012.2867] two of the current authors have developed an entropy bound for equilibrium uncollapsed matter using only classical general relativity, basic thermodynamics, and the Unruh effect. An odd feature of that bound, S <= A/2, was that the proportionality constant, 1/2, was weaker than that expected from black hole thermodynamics, 1/4. In the current article we strengthen the previous results by obtaining a bound involving the (suitably averaged) w parameter. Simple causality arguments restrict this averaged parameter to be <= 1. When equality holds, the entropy bound saturates at the value expected based on black hole thermodynamics. We also add some clarifying comments regarding the (net) positivity of the chemical potential. Overall, we find that even in the absence of any black hole region, we can nevertheless get arbitrarily close to the Bekenstein entropy.Comment: V1: 14 pages. V2: One reference added. V3: This version accepted for publication in JHE

Conformal weights in the Kerr/CFT correspondence

It has been conjectured that a near-extreme Kerr black hole is described by a 2d CFT. Previous work has shown that CFT operators dual to axisymmetric gravitational perturbations have integer conformal weights. In this paper, we study the analogous problem in 5d. We consider the most general near-extreme vacuum black hole with two rotational symmetries. This includes Myers-Perry black holes, black rings and Kaluza-Klein black holes. We find that operators dual to gravitational (or electromagnetic or massless scalar field) perturbations preserving both rotational symmetries have integer conformal weights, the same for all black holes considered.Comment: 19 page

A soliton menagerie in AdS

We explore the behaviour of charged scalar solitons in asymptotically global AdS4 spacetimes. This is motivated in part by attempting to identify under what circumstances such objects can become large relative to the AdS length scale. We demonstrate that such solitons generically do get large and in fact in the planar limit smoothly connect up with the zero temperature limit of planar scalar hair black holes. In particular, for given Lagrangian parameters we encounter multiple branches of solitons: some which are perturbatively connected to the AdS vacuum and surprisingly, some which are not. We explore the phase space of solutions by tuning the charge of the scalar field and changing scalar boundary conditions at AdS asymptopia, finding intriguing critical behaviour as a function of these parameters. We demonstrate these features not only for phenomenologically motivated gravitational Abelian-Higgs models, but also for models that can be consistently embedded into eleven dimensional supergravity.Comment: 62 pages, 21 figures. v2: added refs and comments and updated appendice