396 research outputs found
(2 + 1) noncommutative gravity and conical spacetimes
We solve (2+1) noncommutative gravity coupled to point-like sources. We find
continuity with Einstein gravity since we recover the classical gravitational
field in the limit or at large distance from the source. It
appears a limitation on the mass which is twice than expected. Since the
distance is not gauge invariant, the measure of the deficit angle near the
source is intrinsically ambiguous, with the gauge group playing the role of
statistical ensemble. Einstein determinism can be recovered only at large
distance from the source, compared with the scale of the noncommutative
parameter .Comment: 19 pages, LaTeX, no figure
Classical theta constants vs. lattice theta series, and super string partition functions
Recently, various possible expressions for the vacuum-to-vacuum superstring
amplitudes has been proposed at genus . To compare the different
proposals, here we will present a careful analysis of the comparison between
the two main technical tools adopted to realize the proposals: the classical
theta constants and the lattice theta series. We compute the relevant Fourier
coefficients in order to relate the two spaces. We will prove the equivalence
up to genus 4. In genus five we will show that the solutions are equivalent
modulo the Schottky form and coincide if we impose the vanishing of the
cosmological constant.Comment: 21 page
Noncommutative gravity coupled to fermions: second order expansion via Seiberg-Witten map
We use the Seiberg-Witten map (SW map) to expand noncommutative gravity
coupled to fermions in terms of ordinary commuting fields. The action is
invariant under general coordinate transformations and local Lorentz rotations,
and has the same degrees of freedom as the commutative gravity action. The
expansion is given up to second order in the noncommutativity parameter
{\theta}. A geometric reformulation and generalization of the SW map is
presented that applies to any abelian twist. Compatibility of the map with
hermiticity and charge conjugation conditions is proven. The action is shown to
be real and invariant under charge conjugation at all orders in {\theta}. This
implies the bosonic part of the action to be even in {\theta}, while the
fermionic part is even in {\theta} for Majorana fermions.Comment: 27 pages, LaTeX. Revised version with proof of charge conjugation
symmetry of the NC action and its parity under theta --> - theta (see new
sect. 2.6, sect. 6 and app. B). References added. arXiv admin note:
substantial text overlap with arXiv:0902.381
Equidistribution Rates, Closed String Amplitudes, and the Riemann Hypothesis
We study asymptotic relations connecting unipotent averages of
automorphic forms to their integrals over the moduli space
of principally polarized abelian varieties. We obtain reformulations of the
Riemann hypothesis as a class of problems concerning the computation of the
equidistribution convergence rate in those asymptotic relations. We discuss
applications of our results to closed string amplitudes. Remarkably, the
Riemann hypothesis can be rephrased in terms of ultraviolet relations occurring
in perturbative closed string theory.Comment: 15 page
Gravity on a fuzzy sphere
We propose an action for gravity on a fuzzy sphere, based on a matrix model.
We find striking similarities with an analogous model of two dimensional
gravity on a noncommutative plane, i.e. the solution space of both models is
spanned by pure U(2) gauge transformations acting on the background solution of
the matrix model, and there exist deformations of the classical diffeomorphisms
which preserve the two-dimensional noncommutative gravity actions.Comment: 14 pages, no figures, LaTe
Massive Dirac particles on the background of charged de-Sitter black hole manifolds
We consider the behavior of massive Dirac fields on the background of a
charged de-Sitter black hole. All black hole geometries are taken into account,
including the Reissner-Nordstr\"{o}m-de-Sitter one, the Nariai case and the
ultracold case. Our focus is at first on the existence of bound quantum
mechanical states for the Dirac Hamiltonian on the given backgrounds. In this
respect, we show that in all cases no bound state is allowed, which amounts
also to the non-existence of normalizable time-periodic solutions of the Dirac
equation. This quantum result is in contrast to classical physics, and it is
shown to hold true even for extremal cases. Furthermore, we shift our attention
on the very interesting problem of the quantum discharge of the black holes.
Following Damour-Deruelle-Ruffini approach, we show that the existence of
level-crossing between positive and negative continuous energy states is a
signal of the quantum instability leading to the discharge of the black hole,
and in the cases of the Nariai geometry and of the ultracold geometries we also
calculate in WKB approximation the transmission coefficient related to the
discharge process.Comment: 19 pages, 11 figures. Macro package: Revtex4. Changes concern mainly
the introduction and the final discussion in section VI; moreover, Appendix D
on the evaluation of the Nariai transmission integral has been added.
References adde
Emission of correlated photon pairs from superluminal perturbations in dispersive media
We develop a perturbative theory that describes a superluminal refractive
perturbation propagating in a dispersive medium and the subsequent excitation
of the quantum vacuum zero-point fluctuations. We find a process similar to the
anomalous Doppler effect: photons are emitted in correlated pairs and mainly
within a Cerenkov-like cone, one on the forward and the other in backward
directions. The number of photon pairs emitted from the perturbation increases
strongly with the degree of superluminality and under realizable experimental
conditions, it can reach up to ~0.01 photons per pulse. Moreover, it is in
principle possible to engineer the host medium so as to modify the effective
group refractive index. In the presence of "fast light" media, e.g. a with
group index smaller than unity, a further ~10x enhancement may be achieved and
the photon emission spectrum is characterized by two sharp peaks that, in
future experiments would clearly identify the correlated emission of photon
pairs.Comment: 9 pages, 7 figure
Supersymmetric solutions of gauged five-dimensional supergravity with general matter couplings
We perform the characterization program for the supersymmetric configurations
and solutions of the , Supergravity Theory coupled to an
arbitrary number of vectors, tensors and hypermultiplets and with general
non-Abelian gaugins. By using the conditions yielded by the characterization
program, new exact supersymmetric solutions are found in the
model for the hyperscalars and with as the gauge group. The
solutions also content non-trivial vector and massive tensor fields, the latter
being charged under the U(1) sector of the gauge group and with selfdual
spatial components. These solutions are black holes with
near horizon geometry in the gauged version of the theory and for the ungauged
case we found naked singularities. We also analyze supersymmetric solutions
with only the scalars of the vector/tensor multiplets and the metric
as the non-trivial fields. We find that only in the null class the scalars
can be non-constant and for the case of constant we refine
the classification in terms of the contributions to the scalar potential.Comment: Minor changes in wording and some typos corrected. Version to appear
in Class. Quantum Grav. 38 page
Noncommutative with Quantized Cosmological Constant
We examine a recent deformation of three-dimensional anti-deSitter gravity
based on noncommutative Chern-Simons theory with gauge group . In addition to a noncommutative analogue of 3D gravity, the theory
contains two addition gauge fields which decouple in the commutative limit. It
is well known that the level is quantized in noncommutative Chern-Simons
theory. Here it implies that the cosmological constant goes like minus one over
an integer-squared. We construct the noncommutative vacuum by applying
a Seiberg-Witten map from the commutative case. The procedure is repeated for
the case of a conical space resulting from a massive spinning particle.Comment: 16 p
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