7,010 research outputs found
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 of the Laplace type operators , 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
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
Forms on Vector Bundles Over Hyperbolic Manifolds and the Conformal Anomaly
We study gauge theories based on abelian 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 forms of order up to in spaces of
dimension up to are then calculated.Comment: 13 pages, 2 table
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 , scalar fields in
three-dimensional hyperbolic space (the Euclidean Anti-de Sitter space
), in (the geometry of the Euclidean BTZ black hole), and in
, and the Higgs model in a -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
Forces Produced by Different Nonconventional Bracket or Ligature Systems during Alignment of Apically Displaced Teeth
Objective: To analyze the forces released by four types of passive stainless steel self-ligating brackets (SLBs), and by two nonconventional elastomeric ligature-bracket systems when compared with conventional elastomeric ligatures on conventional stainless steel brackets during the alignment of apically displaced teeth at the maxillary arch. Materials and Methods: An experimental model consisting of five brackets was used to assess the forces released by the seven different ligature-bracket systems with 0.012" or 0.014" super- elastic nickel titanium wire in the presence of different amounts of apical displacement of the canine (ranging from 1.5 mm to 6 mm). Comparisons between the different types of bracket/wire/ ligature systems were carried out by means of ANOVA on ranks with Dunnett's post hoc test (P < .05). Results: When correction of a misalignment greater than 3 mm is attempted, a noticeable amount of force for alignment is generated by passive SLBs and nonconventional elastomeric ligature- bracket systems, and a null amount of force is released in the presence of conventional elasto- meric ligatures on conventional brackets. Conclusions: When minimal apical displacement is needed (1.5 mm), the differences in performance between low-friction and conventional systems are minimal. These differences become significant when correction of a misalignment of greater than 3.0 mm is attempted. © 2009 by The EH Angle Education and Research Foundation, Inc
Propagators and WKB-exactness in the plane wave limit of AdSxS
Green functions for the scalar, spinor and vector fields in a plane wave
geometry arising as a Penrose limit of are obtained. The
Schwinger-DeWitt technique directly gives the results in the plane wave
background, which turns out to be WKB-exact. Therefore the structural
similarity with flat space results is unveiled. In addition, based on the local
character of the Penrose limit, it is claimed that for getting the correct
propagators in the limit one can rely on the first terms of the direct geodesic
contribution in the Schwinger-DeWitt expansion of the original propagators .
This is explicitly shown for the Einstein Static Universe, which has the same
Penrose limit as with equal radii, and for a number of other
illustrative cases.Comment: 18 pages, late
The Feynman propagator for spin foam quantum gravity
We link the notion causality with the orientation of the 2-complex on which
spin foam models are based. We show that all current spin foam models are
orientation-independent, pointing out the mathematical structure behind this
independence. Using the technology of evolution kernels for quantum
fields/particles on Lie groups/homogeneous spaces, we construct a generalised
version of spin foam models, introducing an extra proper time variable and
prove that different ranges of integration for this variable lead to different
classes of spin foam models: the usual ones, interpreted as the quantum gravity
analogue of the Hadamard function of QFT or as a covariant definition of the
inner product between quantum gravity states; and a new class of causal models,
corresponding to the quantum gravity analogue of the Feynman propagator in QFT,
non-trivial function of the orientation data, and implying a notion of
''timeless ordering''.Comment: RevTex, 5 pages, no figures; v2-3:minor typos correcte
Vacuum Polarization in an Anti-de Sitter Space as an Origin for a Cosmological Constant in a Brane World
In this Letter we show that the vacuum polarization of quantum fields in an
anti-de Sitter space naturally gives rise to a small but nonzero cosmological
constant in a brane world living in it. To explain the extremely small ratio of
mass density in the cosmological constant to the Planck mass density in our
universe (\approx 10^{-123}) as suggested by cosmological observations, all we
need is a four-dimensional brane world (our universe) living in a
five-dimensional anti-de Sitter space with a curvature radius r_0 \sim
10^{-3}cm and a fundamental Planck energy M_P \sim 10^9 GeV, and a scalar field
with a mass m \sim r_0^{-1}\sim 10^{-2}eV. Probing gravity down to a scale \sim
10^{-3}cm, which is attainable in the near future, will provide a test of the
model.Comment: 10 pages, including 1 figur
Graviton 1-loop partition function for 3-dimensional massive gravity
The graviton 1-loop partition function in Euclidean topologically massive
gravity (TMG) is calculated using heat kernel techniques. The partition
function does not factorize holomorphically, and at the chiral point it has the
structure expected from a logarithmic conformal field theory. This gives strong
evidence for the proposal that the dual conformal field theory to TMG at the
chiral point is indeed logarithmic. We also generalize our results to new
massive gravity.Comment: 19 pages, v2: major revision, considerably stronger conclusions,
added comparison with LCFT partition function, confirmation of LCFT
conjecture, added autho
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