The flat limit of three dimensional asymptotically anti-de Sitter spacetimes

In order to get a better understanding of holographic properties of gravitational theories with a vanishing cosmological constant, we analyze in detail the relation between asymptotically anti-de Sitter and asymptotically flat spacetimes in three dimensions. This relation is somewhat subtle because the limit of vanishing cosmological constant cannot be naively taken in standard Fefferman-Graham coordinates. After reformulating the standard anti-de Sitter results in Robinson-Trautman coordinates, a suitably modified Penrose limit is shown to connect both asymptotic regimes.Comment: 11 pages revtex fil

p-Brane Dyons and Electric-magnetic Duality

We discuss dyons, charge quantization and electric-magnetic duality for self-interacting, abelian, p-form theories in the spacetime dimensions D=2(p+1) where dyons can be present. The corresponding quantization conditions and duality properties are strikingly different depending on whether p is odd or even. If p is odd one has the familiar eg'-ge'= 2nh, whereas for even p one finds the opposite relative sign, eg'+ge'= 2nh. These conditions are obtained by introducing Dirac strings and taking due account of the multiple connectedness of the configuration space of the strings and the dyons. A two-potential formulation of the theory that treats the electric and magnetic sources on the same footing is also given. Our results hold for arbitrary gauge invariant self-interaction of the fields and are valid irrespective of their duality properties.Comment: 33 pages, 1 figur

A differential geometry approach to asymmetric transmission of light

In the last ten years, the technology of differential geometry, ubiquitous in gravitational physics, has found its place in the field of optics. It has been successfully used in the design of optical metamaterials, through a technique now known as "transformation optics". This method, however, only applies for the particular class of metamaterials known as impedance matched, that is, materials whose electric permittivity is equal to their magnetic permeability. In that case, the material may be described by a spacetime metric. In the present work we will introduce a generalization of the geometric methods of transformation optics to situations in which the material is not impedance matched. In such situation, the material -or more precisely, its constitutive tensor- will not be described by a metric only. We bring in a second tensor, with the local symmetries of the Weyl tensor, the "$W$-tensor". In the geometric optics approximation we show how the properties of the $W$-tensor are related to the asymmetric transmission of the material. We apply this feature into the design of a particularly interesting set of asymmetric materials. These materials are birefringent when light rays approach the material in a given direction, but behave just like vacuum when the rays have the opposite direction with the appropriate polarization (or, in some cases, independently of the polarization)

Decay of the Cosmological Constant. Equivalence of Quantum Tunneling and Thermal Activation in Two Spacetime Dimensions

We study the decay of the cosmological constant in two spacetime dimensions through production of pairs. We show that the same nucleation process looks as quantum mechanical tunneling (instanton) to one Killing observer and as thermal activation (thermalon) to another. Thus, we find another striking example of the deep interplay between gravity, thermodynamics and quantum mechanics which becomes apparent in presence of horizons.Comment: 11 pages, 6 figure

Spin Networks for Non-Compact Groups

Spin networks are natural generalization of Wilson loops functionals. They have been extensively studied in the case where the gauge group is compact and it has been shown that they naturally form a basis of gauge invariant observables. Physically the restriction to compact gauge group is enough for the study of Yang-mills theories, however it is well known that non-compact groups naturally arise as internal gauge groups for Lorentzian gravity models. In this context a proper construction of gauge invariant observables is needed. The purpose of this work is to define the notion of spin network states for non-compact groups. We first built, by a careful gauge fixing procedure, a natural measure and a Hilbert space structure on the space of gauge invariant graph connection. Spin networks are then defined as generalized eigenvectors of a complete set of hermitic commuting operators. We show how the delicate issue of taking the quotient of a space by non compact groups can be address in term of algebraic geometry. We finally construct the full Hilbert space containing all spin network states. Having in mind application to gravity we illustrate our results for the groups SL(2,R), SL(2,C).Comment: 43pages, many figures, some comments adde

Supergravity description of field theories on curved manifolds and a no go theorem

In the first part of this paper we find supergravity solutions corresponding to branes on worldvolumes of the form $R^d \times \Sigma$ where $\Sigma$ is a Riemann surface. These theories arise when we wrap branes on holomorphic Riemann surfaces inside $K3$ or CY manifolds. In some cases the theory at low energies is a conformal field theory with two less dimensions. We find some non-singular supersymmetric compactifications of M-theory down to $AdS_5$. We also propose a criterion for permissible singularities in supergravity solutions. In the second part of this paper, which can be read independently of the first, we show that there are no non-singular Randall-Sundrum or de-Sitter compactifications for large class of gravity theories.Comment: latex, 37 pages. v2: References adde

A 2D Field Theory Equivalent to 3D Gravity with No Cosmological Constant

info:eu-repo/semantics/publishe