42,954 research outputs found
On the Geometric Properties of AdS Instantons
According to the positive energy conjecture of Horowitz and Myers, there is a
specific supergravity solution, AdS soliton, which has minimum energy among all
asymptotically locally AdS solutions with the same boundary conditions. Related
to the issue of semiclassical stability of AdS soliton in the context of pure
gravity with a negative cosmological constant, physical boundary conditions are
determined for an instanton solution which would be responsible for vacuum
decay by barrier penetration. Certain geometric properties of instantons are
studied, using Hermitian differential operators. On a -dimensional
instanton, it is shown that there are harmonic functions. A class of
instanton solutions, obeying more restrictive boundary conditions, is proved to
have Killing vectors which also commute. All but one of the Killing
vectors are duals of harmonic one-forms, which are gradients of harmonic
functions, and do not have any fixed points.Comment: 22 pages, Latex, short comments and a reference adde
Total Mass-Momentum of Arbitrary Initial-Data Sets in General Relativity
For an asymptotically flat initial-data set in general relativity, the total
mass-momentum may be interpreted as a Hermitian quadratic form on the complex,
two-dimensional vector space of ``asymptotic spinors''. We obtain a
generalization to an arbitrary initial-data set. The mass-momentum is retained
as a Hermitian quadratic form, but the space of ``asymptotic spinors'' on which
it is a function is modified. Indeed, the dimension of this space may range
from zero to infinity, depending on the initial data. There is given a variety
of examples and general properties of this generalized mass-momentum.Comment: 25 pages, LaTe
On the Gauged Kahler Isometry in Minimal Supergravity Models of Inflation
In this paper we address the question how to discriminate whether the gauged
isometry group G_Sigma of the Kahler manifold Sigma that produces a D-type
inflaton potential in a Minimal Supergravity Model is elliptic, hyperbolic or
parabolic. We show that the classification of isometries of symmetric cosets
can be extended to non symmetric Sigma.s if these manifolds satisfy additional
mathematical restrictions. The classification criteria established in the
mathematical literature are coherent with simple criteria formulated in terms
of the asymptotic behavior of the Kahler potential K(C) = 2 J(C) where the real
scalar field C encodes the inflaton field. As a by product of our analysis we
show that phenomenologically admissible potentials for the description of
inflation and in particular alpha-attractors are mostly obtained from the
gauging of a parabolic isometry, this being, in particular the case of the
Starobinsky model. Yet at least one exception exists of an elliptic
alpha-attractor, so that neither type of isometry can be a priori excluded. The
requirement of regularity of the manifold Sigma poses instead strong
constraints on the alpha-attractors and reduces their space considerably.
Curiously there is a unique integrable alpha-attractor corresponding to a
particular value of this parameter.Comment: 85 pages, LaTex, 32 jpg figures, 4 tables; v2: title and abstract
slightly modified, some assessments improved and made more precise, two
figures and one reference added, several misprints correcte
Ap\'ery Polynomials and the multivariate Saddle Point Method
The Ap\'ery polynomials and in particular their asymptotic behavior play an
essential role in the understanding of the irrationality of \zeta(3). In this
paper, we present a method to study the asymptotic behavior of the sequence of
the Ap\'ery polynomials ((B_{n})_{n=1}^{\infty}) in the whole complex plane as
(n\rightarrow \infty). The proofs are based on a multivariate version of the
complex saddle point method. Moreover, the asymptotic zero distributions for
the polynomials ((B_{n})_{n=1}^{\infty}) and for some transformed Ap\'ery
polynomials are derived by means of the theory of logarithmic potentials with
external fields, establishing a characterization as the unique solution of a
weighted equilibrium problem. The method applied is a general one, so that the
treatment can serve as a model for the study of objects related to the Ap\'ery
polynomials.Comment: 19 page
Asymptotic Properties of Approximate Bayesian Computation
Approximate Bayesian computation allows for statistical analysis in models
with intractable likelihoods. In this paper we consider the asymptotic
behaviour of the posterior distribution obtained by this method. We give
general results on the rate at which the posterior distribution concentrates on
sets containing the true parameter, its limiting shape, and the asymptotic
distribution of the posterior mean. These results hold under given rates for
the tolerance used within the method, mild regularity conditions on the summary
statistics, and a condition linked to identification of the true parameters.
Implications for practitioners are discussed.Comment: This 31 pages paper is a revised version of the paper, including
supplementary materia
Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy
We study the asymptotic time behavior of global smooth solutions to general
entropy dissipative hyperbolic systems of balance law in m space dimensions,
under the Shizuta-Kawashima condition. We show that these solutions approach
constant equilibrium state in the Lp-norm at a rate O(t^(-m/2(1-1/p))), as t
tends to , for p in [min (m,2),+ \infty]. Moreover, we can show that we
can approximate, with a faster order of convergence, theconservative part of
the solution in terms of the linearized hyperbolic operator for m >= 2, and by
a parabolic equation in the spirit of Chapman-Enskog expansion. The main tool
is given by a detailed analysis of the Green function for the linearized
problem
Dispersion Relations for Electroweak Observables in Composite Higgs Models
We derive dispersion relations for the electroweak oblique observables
measured at LEP in the context of composite Higgs models. It is
shown how these relations can be used and must be modified when modeling the
spectral functions through a low-energy effective description of the strong
dynamics. The dispersion relation for the parameter is then used
to estimate the contribution from spin-1 resonances at the 1-loop level.
Finally, it is shown that the sign of the contribution to the
parameter from the lowest-lying spin-1 states is not necessarily positive
definite, but depends on the energy scale at which the asymptotic behavior of
current correlators is attained.Comment: 34 pages, 4 figures. v2: a few minor changes, typos corrected, list
of references revise
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