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 $A_{N-1}$ 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 $AdS_3\times S^3/\mathbb{Z}_N$ and $AdS_3\times S^3$ 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 $AdS_5\times S^5/\mathbb{Z}_N$ and $AdS_5\times S^5$ geometries. The field theory interpretation is that of an N=2 $SU(n)^N$ 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 $USp(n)$. The corresponding geometries are $AdS_5\times S^5/(\mathbb{Z}_N\times \mathbb{Z}_2)$ and $AdS_5\times S^5/\mathbb{Z}_2$, 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 $AdS_5\times S^5/(\mathbb{Z}_N\times \mathbb{Z}_2)$ and $AdS_5\times S^5/(\mathbb{Z}_M\times \mathbb{Z}_2)$. 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 $n>1$, 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