14,581 research outputs found
Quantum Topological Invariants, Gravitational Instantons and the Topological Embedding
Certain topological invariants of the moduli space of gravitational
instantons are defined and studied. Several amplitudes of two and four
dimensional topological gravity are computed. A notion of puncture in four
dimensions, that is particularly meaningful in the class of Weyl instantons, is
introduced. The topological embedding, a theoretical framework for constructing
physical amplitudes that are well-defined order by order in perturbation theory
around instantons, is explicitly applied to the computation of the correlation
functions of Dirac fermions in a punctured gravitational background, as well as
to the most general QED and QCD amplitude. Various alternatives are worked out,
discussed and compared. The quantum background affects the propagation by
generating a certain effective ``quantum'' metric. The topological embedding
could represent a new chapter of quantum field theory.Comment: LaTeX, 18 pages, no figur
Anyons in Geometric Models of Matter
We show that the "geometric models of matter" approach proposed by the first
author can be used to construct models of anyon quasiparticles with fractional
quantum numbers, using 4-dimensional edge-cone orbifold geometries with
orbifold singularities along embedded 2-dimensional surfaces. The anyon states
arise through the braid representation of surface braids wrapped around the
orbifold singularities, coming from multisections of the orbifold normal bundle
of the embedded surface. We show that the resulting braid representations can
give rise to a universal quantum computer.Comment: 22 pages LaTe
Hamiltonian Analysis of Plebanski Theory
We study the Hamiltonian formulation of Plebanski theory in both the
Euclidean and Lorentzian cases. A careful analysis of the constraints shows
that the system is non regular, i.e. the rank of the Dirac matrix is
non-constant on the non-reduced phase space. We identify the gravitational and
topological sectors which are regular sub-spaces of the non-reduced phase
space. The theory can be restricted to the regular subspace which contains the
gravitational sector. We explicitly identify first and second class constraints
in this case. We compute the determinant of the Dirac matrix and the natural
measure for the path integral of the Plebanski theory (restricted to the
gravitational sector). This measure is the analogue of the
Leutwyler-Fradkin-Vilkovisky measure of quantum gravity.Comment: 25 pages, no figures, references adde
Towards a Gravitational Analog to S-duality in Non-abelian Gauge Theories
For non-abelian non-supersymmetric gauge theories, generic dual theories have
been constructed. In these theories the couplings appear inverted. However,
they do not possess a Yang-Mills structure but rather are a kind of non-linear
sigma model. It is shown that for a topological gravitational model an analog
to this duality exists.Comment: LaTeX, 14 pages, no figures, minor correction
Energy in higher-derivative gravity via topological regularization
Indexación: Scopus.We give a novel definition of gravitational energy for an arbitrary theory of gravity including quadratic-curvature corrections to Einstein's equations. We focus on the theory in four dimensions, in the presence of a negative cosmological constant, and with asymptotically anti-de Sitter (AdS) boundary conditions. As a first example, we compute the gravitational energy and angular momentum of Schwarzschild-AdS black holes, for which we obtain results consistent with previous computations performed using different methods. However, our method is qualitatively different due to the fact that it is intrinsically nonlinear. It relies on the idea of adding to the gravity action topological invariant terms which suffice to regularize the Noether charges and render the variational problem well-posed. This is an idea that has been previously considered in the case of second-order theories, such as general relativity and which, as shown here, extends to higher-derivative theories. Besides black holes, we consider other solutions such as gravitational waves in AdS, for which we also find results that are in agreement. This enables us to investigate the consistency of this approach in the non-Einstein sector of the theory. © 2018 authors. Published by the American Physical Society.https://journals.aps.org/prd/abstract/10.1103/PhysRevD.98.04404
Exact Gravitational Quasinormal Frequencies of Topological Black Holes
We compute the exact gravitational quasinormal frequencies for massless
topological black holes in d-dimensional anti-de Sitter space. Using the gauge
invariant formalism for gravitational perturbations derived by Kodama and
Ishibashi, we show that in all cases the scalar, vector, and tensor modes can
be reduced to a simple scalar field equation. This equation is exactly solvable
in terms of hypergeometric functions, thus allowing an exact analytic
determination of the gravitational quasinormal frequencies.Comment: 14 pages, Latex; v2 additional reference
Quantum Gravity: Has Spacetime Quantum Properties?
The incompatibility between GR and QM is generally seen as a sufficient
motivation for the development of a theory of Quantum Gravity. If - so a
typical argumentation - QM gives a universally valid basis for the description
of all natural systems, then the gravitational field should have quantum
properties. Together with the arguments against semi-classical theories of
gravity, this leads to a strategy which takes a quantization of GR as the
natural avenue to Quantum Gravity. And a quantization of the gravitational
field would in some sense correspond to a quantization of geometry. Spacetime
would have quantum properties. But, this strategy will only be successful, if
gravity is a fundamental interaction. - What, if gravity is instead an
intrinsically classical phenomenon? Then, if QM is nevertheless fundamentally
valid, gravity can not be a fundamental interaction. An intrinsically classical
gravity in a quantum world would have to be an emergent, induced or residual,
macroscopic effect, caused by other interactions. The gravitational field (as
well as spacetime) would not have any quantum properties. A quantization of GR
would lead to artifacts without any relation to nature. The serious problems of
all approaches to Quantum Gravity that start from a direct quantization of GR
or try to capture the quantum properties of gravity in form of a 'graviton'
dynamics - together with the, meanwhile, rich spectrum of approaches to an
emergent gravity and/or spacetime - make this latter option more and more
interesting for the development of a theory of Quantum Gravity. The most
advanced emergent gravity (and spacetime) scenarios are of an
information-theoretical, quantum-computational type.Comment: 31 page
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