Vacuum Polarisation and the Black Hole Singularity

In order to investigate the effects of vacuum polarisation on mass inflation singularities, we study a simple toy model of a charged black hole with cross flowing radial null dust which is homogeneous in the black hole interior. In the region $r^2 \ll e^2$ we find an approximate analytic solution to the classical field equations. The renormalized stress-energy tensor is evaluated on this background and we find the vacuum polarisation backreaction corrections to the mass function $m(r)$. Asymptotic analysis of the semiclassical mass function shows that the mass inflation singularity is much stronger in the presence of vacuum polarisation than in the classical case.Comment: 12 pages, RevTe

Quantum Field Theory of Open Spin Networks and New Spin Foam Models

We describe how a spin-foam state sum model can be reformulated as a quantum field theory of spin networks, such that the Feynman diagrams of that field theory are the spin-foam amplitudes. In the case of open spin networks, we obtain a new type of state-sum models, which we call the matter spin foam models. In this type of state-sum models, one labels both the faces and the edges of the dual two-complex for a manifold triangulation with the simple objects from a tensor category. In the case of Lie groups, such a model corresponds to a quantization of a theory whose fields are the principal bundle connection and the sections of the associated vector bundles. We briefly discuss the relevance of the matter spin foam models for quantum gravity and for topological quantum field theories.Comment: 13 pages, based on the talk given at the X-th Oporto Meeting on Geometry, Physics and Topology, Porto, September 20-24, 200

The metric at infinity on Damek-Ricci spaces

Let S = N A be a Damek-Ricci space, identified with the unit ball B in s via the Cayley transform. Let Sp+q = partial derivative B be the unit sphere in s, p = dimv, q = dimz. The metric in the ball model was computed in [1] both in Euclidean (or geodesic) polar coordinates and in Cartesian coordinates on B. The induced metric on the Euclidean sphere S(R) of radius R is the sum of a constant curvature term, plus a correction term proportional to h(1), where h1 is a suitable differential expression which is smooth on S(R) for R < 1, but becomes (possibly) singular on the unit sphere at the pole (0, 0, 1). It has a simple geometric interpretation, namely h1 = vertical bar Theta vertical bar(2), where Theta is, up to a conformal factor, the pull-back of the canonical 1-form on the group N (defining the horizontal distribution on N) by the generalized stereographic projection. In the symmetric case h(1), as well as the transported distribution on Sp+q {(0, 0, 1)}, have a smooth extension to the whole sphere. This can be interpreted by the Hopf fibration of Sp+q. In the general case no such structure is allowed on the unit sphere, and the question was left open in [1] whether or not h1 extends smoothly at the pole. In this paper we prove that h(1) does not extend, except in the symmetric case. More precisely, writing h(1) in the coordinates (V, Z) on Sp+q as h(1) = Sigma h(ij)((z)) + dz(i) dz j + Sigma h(ij)((v)) dv(i) dv(j) + Sigma h(ij)((zv)) dz(i) dv(j), we prove that, in the non-symmetric case, the coefficients h(ij)((z)) do not have a limit at the pole, but remain bounded there, whereas the coefficients h(ij)((v)) and h(ij)((zv)) extend smoothly at the pole. In order to do this, we obtain an explicit formula for the 1-form Theta valid for any Damek-Ricci space. From this formula we deduce that Theta does not extend to the pole, except for q = 1 (Hermitian symmetric case). The square of Theta and the distribution ker Theta do not extend, unless S is symmetric. Indeed, we prove that the singular part of h(1) vanishes identically if and only if the J(2)-condition holds

The Heat Kernel on AdSAdS

We explicitly evaluate the heat kernel for the Laplacian of arbitrary spin tensor fields on the thermal quotient of (Euclidean) $AdS_N$ for $N\geq 3$ using the group theoretic techniques employed for $AdS_3$ in arXiv:0911.5085. Our approach is general and can be used, in principle, for other quotients as well as other symmetric spaces.Comment: Added references, added appendix on heat kernel in even dimensio

The Heat Kernel on AdS_3 and its Applications

We derive the heat kernel for arbitrary tensor fields on S^3 and (Euclidean) AdS_3 using a group theoretic approach. We use these results to also obtain the heat kernel on certain quotients of these spaces. In particular, we give a simple, explicit expression for the one loop determinant for a field of arbitrary spin s in thermal AdS_3. We apply this to the calculation of the one loop partition function of N=1 supergravity on AdS_3. We find that the answer factorizes into left- and right-moving super Virasoro characters built on the SL(2, C) invariant vacuum, as argued by Maloney and Witten on general grounds.Comment: 46 pages, LaTeX, v2: Reference adde

Renormalization group irreversible functions in more than two dimensions

There are two general irreversibility theorems for the renormalization group in more than two dimensions: the first one is of entropic nature, while the second one, by Forte and Latorre, relies on the properties of the stress-tensor trace, and has been recently questioned by Osborn and Shore. We start by establishing under what assumptions this second theorem can still be valid. Then it is compared with the entropic theorem and shown to be essentially equivalent. However, since the irreversible function of the (corrected) Forte-Latorre theorem is non universal (whereas the relative entropy of the other theorem is universal), it needs the additional step of renormalization. On the other hand, the irreversibility theorem is only guaranteed to be unambiguous if the integral of the stress-tensor trace correlator is finite, which happens for free theories only in dimension smaller than four.Comment: 4 pages; minor changes to improve readability; to appear in Phys. Rev.

The Conformal Anomaly in General Rank 1 Symmetric Spaces and Associated Operator Product

We compute the one-loop effective action and the conformal anomaly associated with the product $\bigotimes_p{\cal L}_p$ of the Laplace type operators ${\cal L}_p, p=1,2$, acting in irreducible rank 1 symmetric spaces of non-compact type. The explicit form of the zeta functions and the conformal anomaly of the stress-energy momentum tensor is derived.Comment: 10 pages, LaTe

An approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions

In this paper, we provide an approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions and discuss the application of this approach in some physical problems. Concretely, we construct the equations for these three quantities; this allows us to achieve them by directly solving equations. In order to construct the equations, we introduce shifted local one-loop effective actions, shifted local vacuum energies, and local spectral counting functions. We solve the equations of one-loop effective actions, vacuum energies, and spectral counting functions for free massive scalar fields in $\mathbb{R}^{n}$, scalar fields in three-dimensional hyperbolic space $H_{3}$ (the Euclidean Anti-de Sitter space $AdS_{3}$), in $H_{3}/Z$ (the geometry of the Euclidean BTZ black hole), and in $S^{1}$, and the Higgs model in a $(1+1)$-dimensional finite interval. Moreover, in the above cases, we also calculate the spectra from the counting functions. Besides exact solutions, we give a general discussion on approximate solutions and construct the general series expansion for one-loop effective actions, vacuum energies, and spectral counting functions. In doing this, we encounter divergences. In order to remove the divergences, renormalization procedures are used. In this approach, these three physical quantities are regarded as spectral functions in the spectral problem.Comment: 37 pages, no figure. This is an enlarged and improved version of the paper published in JHE

Forms on Vector Bundles Over Hyperbolic Manifolds and the Conformal Anomaly

We study gauge theories based on abelian $p-$forms on real compact hyperbolic manifolds. An explicit formula for the conformal anomaly corresponding to skew--symmetric tensor fields is obtained, by using zeta--function regularization and the trace tensor kernel formula. Explicit exact and numerical values of the anomaly for $p-$forms of order up to $p=4$ in spaces of dimension up to $n=10$ are then calculated.Comment: 13 pages, 2 table

Missing the guidewire: an avoidable complication

Central venous catheterization is an imperative tool in the critically ill patient to administer fluids, medications and for monitoring the central venous pressure. This procedure is associated with a variety of complications, some of which can be life threatening. In this brief report, we are addressing one of the rare complications of central venous catheterization which is missing the guidewire. We also described several precautions to avoid this complication as well as modifications in the guidewire to prevent its escape