Orbifold resolutions with general profile

A very general class of resolved versions of the C/Z_N, T^2/Z_N and S^1/Z_2 orbifolds is considered and the free theory of 6D chiral fermions studied on it. As the orbifold limit is taken, localized 4D chiral massless fermions are seen to arise at the fixed points. Their number, location and chirality is found to be independent on the detailed profile of the resolving space and to agree with the result of hep-th/0409229, in which a particular resolution was employed. As a consistency check of the resolution procedure, the massive equation is numerically studied. In particular, for S^1/Z_2, the "resolved" mass--spectrum and wave functions in the internal space are seen to correctly reproduce the usual orbifold ones, as the orbifold limit is taken.Comment: 28 pages, 3 figures, typos corrected, references adde

Modulus stabilization of generalized Randall Sundrum model with bulk scalar field

We study the stabilization of inter-brane spacing modulus of generalized warped brane models with a nonzero brane cosmological constant. Employing Goldberger-Wise stabilization prescription of brane world models with a bulk scalar field, we show that the stabilized value of the modulus generally depends on the value of the brane cosmological constant. Our result further reveals that the stabilized modulus value corresponding to a vanishingly small cosmological constant can only resolve the gauge hierarchy problem simultaneously. This in turn vindicates the original Randall-Sundrum model where the 3-brane cosmological constant was chosen to be zero.Comment: 12 Pages, 1 figure, Revtex, Version to appear in Euro. Phys. Let

Geometry of deformations of branes in warped backgrounds

The `braneworld' (described by the usual worldvolume action) is a D dimensional timelike surface embedded in a N dimensional ($N>D$) warped, nonfactorisable spacetime. We first address the conditions on the warp factor required to have an extremal flat brane in a five dimensional background. Subsequently, we deal with normal deformations of such extremal branes. The ensuing Jacobi equations are analysed to obtain the stability condition. It turns out that to have a stable brane, the warp factor should have a minimum at the location of the brane in the given background spacetime. To illustrate our results we explicitly check the extremality and stability criteria for a few known co-dimension one braneworld models. Generalisations of the above formalism for the cases of (i) curved branes (ii) asymmetrical warping and (iii) higher co-dimension braneworlds are then presented alongwith some typical examples for each. Finally, we summarize our results and provide perspectives for future work along these lines.Comment: 21 pages. Version matching final version. Accepted for publication in Class. Quant. Gra

Can degenerate bound states occur in one dimensional quantum mechanics?

We point out that bound states, degenerate in energy but differing in parity, may form in one dimensional quantum systems even if the potential is non-singular in any finite domain. Such potentials are necessarily unbounded from below at infinity and occur in several different contexts, such as in the study of localised states in brane-world scenarios. We describe how to construct large classes of such potentials and give explicit analytic expressions for the degenerate bound states. Some of these bound states occur above the potential maximum while some are below. Various unusual features of the bound states are described and after highlighting those that are ansatz independent, we suggest that it might be possible to observe such parity-paired degenerate bound states in specific mesoscopic systems.Comment: 10 pages, 2 figures, to appear in Europhysics Letter

de Sitter branes with a bulk scalar

We propose new braneworld models arising from a scalar field in the bulk. In these examples, the induced on--brane line element is de Sitter (or anti de Sitter) and the bulk (five dimensional) Einstein equations can be exactly solved to obtain warped spacetimes. The solutions thus derived are single and two-brane models -- one with {\em thin} branes while the other one of the {\em thick} variety. The field profiles and the potentials are obtained and analysed for each case. We note that for the {\em thick} brane scenario the field profile resembles a kink, whereas for one or more {\em thin} branes, it is finite and bounded in the domain of the extra dimension. We have also addressed the localisation of gravity and other matter fields on the brane for these braneworld models.Comment: 18 pages, 5 figures. Substantial changes and new results. To appear in GR

Braneworlds in six dimensions: new models with bulk scalars

Six dimensional bulk spacetimes with 3-- and 4--branes are constructed using certain non--conventional bulk scalars as sources. In particular, we investigate the consequences of having the phantom (negative kinetic energy) and the Brans--Dicke scalar in the bulk while obtaining such solutions. We find geometries with 4--branes with a compact on--brane dimension (hybrid compactification) which may be assumed to be small in order to realize a 3--brane world. On the other hand, we also construct, with similar sources, bulk spacetimes where a 3--brane is located at a conical singularity. Furthermore, we investigate the issue of localization of matter fields (scalar, fermion, graviton, vector) on these 3-- and 4--branes and conclude with comments on our six dimensional models.Comment: 24 pages, 1 figure, Replaced to match version published in Class. Quant. Gra

Particle creation in the presence of a warped extra dimension

Particle creation in spacetimes with a warped extra dimension is studied. In particular, we investigate the dynamics of a conformally coupled, massless scalar field in a five dimensional warped geometry where the induced metric on the 3--branes is that of a spatially flat cosmological model. We look at situations where the scale of the extra dimension is assumed (i) to be time independent or (ii) to have specific functional forms for time dependence. The warp factor is chosen to be that of the Randall--Sundrum model. With particular choices for the functional form of the scale factor (and also the function characterising the time evolution of the extra dimension) we obtain the ${| \beta_k|}^2$, the particle number and energy densities after solving (wherever possible, analytically but, otherwise, numerically) the conformal scalar field equations. The behaviour of these quantities for the massless and massive Kaluza--Klein modes are examined. Our results show the effect of a warped extra dimension on particle creation and illustrate how the nature of particle production on the brane depends on the nature of warping, type of cosmological evolution as well as the temporal evolution of the extra dimension.Comment: 21 pages, 10 figures, minor corrections, new references added, version to appear in JCA

Scalar kinks and fermion localisation in warped spacetimes

Scalar kinks propagating along the bulk in warped spacetimes provide a thick brane realisation of the braneworld. We consider here, a class of such exact solutions of the full Einstein-scalar system with a sine-Gordon potential and a negative cosmological constant. In the background of the kink and the corresponding warped geometry, we discuss the issue of localisation of spin half fermions (with emphasis on massive ones) on the brane in the presence of different types of kink-fermion Yukawa couplings. We analyse the possibility of quasi-bound states for large values of the Yukawa coupling parameter $\gamma_F$ (with $\nu$, the warp factor parameter kept fixed) using appropriate, recently developed, approximation methods. In particular, the spectrum of the low--lying states and their lifetimes are obtained, with the latter being exponentially enhanced for large $\nu \gamma_F$. Our results indicate quantitatively, within this model, that it is possible to tune the nature of warping and the strength and form of the Yukawa interaction to obtain trapped massive fermion states on the brane, which, however, do have a finite (but very small) probability of escaping into the bulk.Comment: 22 pages, 4 figures, RevTex

Splitting of degenerate states in one-dimensional quantum mechanics

10.1140/epjp/i2012-12028-8European Physical Journal Plus12731-