56 research outputs found
The Dirac field in Taub-NUT background
We investigate the SO(4,1) gauge-invariant theory of the Dirac fermions in
the external field of the Kaluza-Klein monopole, pointing out that the quantum
modes can be recovered from a Klein-Gordon equation analogous to the Schr\"
odinger equation in the Taub-NUT background. Moreover, we show that there is a
large collection of observables that can be directly derived from those of the
scalar theory. These offer many possibilities of choosing complete sets of
commuting operators which determine the quantum modes. In addition there are
some spin- like and Dirac-type operators involving the covariantly constant
Killing-Yano tensors of the hyper-K\" ahler Taub-NUT space. The energy
eigenspinors of the central modes in spherical coordinates are completely
evaluated in explicit, closed form.Comment: 20 pages, latex, no figure
Brane inflation and the fine-tuning problem
Brane inflation can provide a promissing framework for solving the
fine-tuning problem in standard inflationary models. The aim of this paper is
to illustrate the mechanism by which this can be achieved. By considering the
supersymmetric two-stage inflation model it is shown that the initial
fine-tuning of the coupling parameter can be considerably relaxed. SubPlanckian
values of the inflaton during inflation can also be obtained.Comment: 04 pages (Revtex
Dynamical algebra and Dirac quantum modes in Taub-NUT background
The SO(4,1) gauge-invariant theory of the Dirac fermions in the external
field of the Kaluza-Klein monopole is investigated. It is shown that the
discrete quantum modes are governed by reducible representations of the o(4)
dynamical algebra generated by the components of the angular momentum operator
and those of the Runge-Lenz operator of the Dirac theory in Taub-NUT
background. The consequence is that there exist central and axial discrete
modes whose spinors have no separated variables.Comment: 17 pages, latex, no figures. Version to appear in Class.Quantum Gra
Saddle-point dynamics of a Yang-Mills field on the exterior Schwarzschild spacetime
We consider the Cauchy problem for a spherically symmetric SU(2) Yang-Mills
field propagating outside the Schwarzschild black hole. Although solutions
starting from smooth finite energy initial data remain smooth for all times,
not all of them scatter since there are non-generic solutions which
asymptotically tend to unstable static solutions. We show that a static
solution with one unstable mode appears as an intermediate attractor in the
evolution of initial data near a border between basins of attraction of two
different vacuum states. We study the saddle-point dynamics near this
attractor, in particular we identify the universal phases of evolution: the
ringdown approach, the exponential departure, and the eventual decay to one of
the vacuum states.Comment: 15 pages, 5 figure
Symmetries of the Dirac operators associated with covariantly constant Killing-Yano tensors
The continuous and discrete symmetries of the Dirac-type operators produced
by particular Killing-Yano tensors are studied in manifolds of arbitrary
dimensions. The Killing-Yano tensors considered are covariantly constant and
realize certain square roots of the metric tensor. Such a Killing-Yano tensor
produces simultaneously a Dirac-type operator and the generator of a
one-parameter Lie group connecting this operator with the standard Dirac one.
The Dirac operators are related among themselves through continuous or discrete
transformations. It is shown that the groups of the continuous symmetry can be
only U(1) and SU(2), specific to (hyper-)Kahler spaces, but arising even in
cases when the requirements for these special geometries are not fulfilled. The
discrete symmetries are also studied obtaining the discrete groups Z_4 and Q.
The briefly presented examples are the Euclidean Taub-NUT space and the
Minkowski spacetime.Comment: 27 pages, latex, no figures, final version to be published in Class.
Quantum Gravit
Gravitating sphalerons and sphaleron black holes in asymptotically anti-de Sitter spacetime
Numerical arguments are presented for the existence of spherically symmetric
regular and black hole solutions of the EYMH equations with a negative
cosmological constant. These solutions approach asymptotically the anti-de
Sitter spacetime. The main properties of the solutions and the differences with
respect to the asymptotically flat case are discussed. The instability of the
gravitating sphaleron solutions is also proven.Comment: 30 pages, LaTeX, 8 Encapsulated PostScript figure
Classical Yang-Mills Black hole hair in anti-de Sitter space
The properties of hairy black holes in Einstein–Yang–Mills (EYM) theory are reviewed, focusing on spherically symmetric solutions. In particular, in asymptotically anti-de Sitter space (adS) stable black hole hair is known to exist for frak su(2) EYM. We review recent work in which it is shown that stable hair also exists in frak su(N) EYM for arbitrary N, so that there is no upper limit on how much stable hair a black hole in adS can possess
Gravitational and Yang-Mills instantons in holographic RG flows
We study various holographic RG flow solutions involving warped
asymptotically locally Euclidean (ALE) spaces of type. A
two-dimensional RG flow from a UV (2,0) CFT to a (4,0) CFT in the IR is found
in the context of (1,0) six dimensional supergravity, interpolating between
and geometries. We also find
solutions involving non trivial gauge fields in the form of SU(2) Yang-Mills
instantons on ALE spaces. Both flows are of vev type, driven by a vacuum
expectation value of a marginal operator. RG flows in four dimensional field
theories are studied in the type IIB and type I context. In type IIB theory,
the flow interpolates between and geometries. The field theory interpretation is that of an N=2
quiver gauge theory flowing to N=4 SU(n) gauge theory. In type I theory the
solution describes an RG flow from N=2 quiver gauge theory with a product gauge
group to N=2 gauge theory in the IR, with gauge group . The
corresponding geometries are and , respectively. We also
explore more general RG flows, in which both the UV and IR CFTs are N=2 quiver
gauge theories and the corresponding geometries are and . Finally, we discuss the matching between the geometric and
field theoretic pictures of the flows.Comment: 32 pages, 3 figures, typoe corrected and a reference adde
Static axially symmetric solutions of Einstein-Yang-Mills equations with a negative cosmological constant: the regular case
Numerical solutions of the Einstein-Yang-Mills equations with a negative
cosmological constant are constructed. These axially symmetric solutions
approach asymptotically the anti-de Sitter spacetime and are regular
everywhere. They are characterized by the winding number , the mass and
the non-Abelian magnetic charge. The main properties of the solutions and the
differences with respect to the asymptotically flat case are discussed. The
existence of axially symmetric monopole and dyon solutions in fixed anti-de
Sitter spacetime is also discussed.Comment: 55 pages, 38 Encapsulated PostScript figures; high-resolution figures
are available on reques
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