Gravity on an extended brane in six-dimensional warped flux compactifications

We study linearized gravity in a six-dimensional Einstein-Maxwell model of warped braneworlds, where the extra dimensions are compactified by a magnetic flux. It is difficult to construct a strict codimension two braneworld with matter sources other than pure tension. To overcome this problem we replace the codimension two defect by an extended brane, with one spatial dimension compactified on a Kaluza-Klein circle. Our background is composed of a warped, axisymmetric bulk and one or two branes. We find that weak gravity sourced by arbitrary matter on the brane(s) is described by a four-dimensional scalar-tensor theory. We show, however, that the scalar mode is suppressed at long distances and hence four-dimensional Einstein gravity is reproduced on the brane.Comment: 20 pages, 7 figures; v2: references and comments added; v3: version published in Physical Review

S-matrices for spinor particles on Reissner-Nordstr\"{o}m black holes

The scattering problems arising when considering the contribution of the topologically inequivalent configurations of the spinors on Reissner-Nordstr\"{o}m black holes to the Hawking radiation are correctly stated. The corresponding $S$-matrices are described and presented in the form convenient to numerical computations.Comment: 11 pages, LaTe

Color Superconductivity in N=2 Supersymmetric Gauge Theories

We study vacuum structure of N=2 supersymmetric (SUSY) QCD, based on the gauge group SU(2) with N_f=2 flavors of massive hypermultiplet quarks, in the presence of non-zero baryon chemical potential (\mu). The theory has a classical vacuum preserving baryon number symmetry, when a mass term, which breaks N=2 SUSY but preserves N=1 SUSY, for the adjoint gauge chiral multiplet (m_{ad}) is introduced. By using the exact result of N=2 SUSY QCD, we analyze low energy effective potential at the leading order of perturbation with respect to small SUSY breaking parameters, \mu and m_{ad}. We find that the baryon number is broken as a consequence of the SU(2) strong gauge dynamics, so that color superconductivity dynamically takes place at the non-SUSY vacuum.Comment: 15 pages, 9 figures, a figure and discussions added in Sec. 4, version to appear in Phys. Rev.

Cosmological evolution of regularized branes in 6D warped flux compactifications

We study the cosmological evolution of extended branes in 6D warped flux compactification models. The branes are endowed with the three ordinary spatial dimensions, which are assumed to be homogeneous and isotropic, as well as an internal extra dimension compactified on a circle. We embed these codimension 1 branes in a static bulk 6D spacetime, whose geometry is a solution of 6D Einstein-Maxwell or Einstein-Maxwell-dilaton theories, corresponding to a warped flux compactification. The brane matter consists of a complex scalar field which is coupled to the bulk U(1) gauge field. In both models, we show that there is critical point which the brane cannot cross as it moves in the bulk. We study the cosmological behaviour, especially when the brane approaches this critical point or one of the two conical singularities. In the present setup where the bulk geometry is fixed, we find that the brane cosmology does not coincide with the standard one in the low energy limit.Comment: 14 pages, 4 figures, references and discussions added, to appear in PR

Static and symmetric wormholes respecting energy conditions in Einstein-Gauss-Bonnet gravity

Properties of $n(\ge 5)$-dimensional static wormhole solutions are investigated in Einstein-Gauss-Bonnet gravity with or without a cosmological constant $\Lambda$. We assume that the spacetime has symmetries corresponding to the isometries of an $(n-2)$-dimensional maximally symmetric space with the sectional curvature $k=\pm 1, 0$. It is also assumed that the metric is at least $C^{2}$ and the $(n-2)$-dimensional maximally symmetric subspace is compact. Depending on the existence or absence of the general relativistic limit $\alpha \to 0$, solutions are classified into general relativistic (GR) and non-GR branches, respectively, where $\alpha$ is the Gauss-Bonnet coupling constant. We show that a wormhole throat respecting the dominant energy condition coincides with a branch surface in the GR branch, otherwise the null energy condition is violated there. In the non-GR branch, it is shown that there is no wormhole solution for $k\alpha \ge 0$. For the matter field with zero tangential pressure, it is also shown in the non-GR branch with $k\alpha<0$ and $\Lambda \le 0$ that the dominant energy condition holds at the wormhole throat if the radius of the throat satisfies some inequality. In the vacuum case, a fine-tuning of the coupling constants is shown to be necessary and the radius of a wormhole throat is fixed. Explicit wormhole solutions respecting the energy conditions in the whole spacetime are obtained in the vacuum and dust cases with $k=-1$ and $\alpha>0$.Comment: 10 pages, 2 tables; v2, typos corrected, references added; v3, interpretation of the solution for n=5 in section IV corrected; v4, a very final version to appear in Physical Review

Bulk scalar emission from a rotating black hole pierced by a tense brane

We study the emission of scalar fields into the bulk from a six-dimensional rotating black hole pierced by a 3-brane. We determine the angular eigenvalues in the presence of finite brane tension by using the continued fraction method. The radial equation is integrated numerically, giving the absorption probability (graybody factor) in a wider frequency range than in the preexisting literature. We then compute the power and angular momentum emission spectra for different values of the rotation parameter and brane tension, and compare their relative behavior in detail. As is expected from the earlier result for a nonrotating black hole, the finite brane tension suppresses the emission rates. As the rotation parameter increases, the power spectra are reduced at low frequencies due to the smaller Hawking temperature and are enhanced at high frequencies due to superradiance. The angular momentum spectra are enhanced over the whole frequency range as the rotation parameter increases. The spectra and the amounts of energy and angular momentum radiated away into the bulk are thus determined by the interplay of these effects.Comment: 10 pages, 7 figures; v2: references added; v3: Figs. 4, 5, 6 corrected. Numerical results changed; v4: references added, minor clarification, accepted for publication in Physical Review

Field localization on a brane intersection in anti-de Sitter spacetime

We discuss the localization of scalar, fermion, and gauge field zero modes on a $3-$brane that resides at the intersection of two $4-$branes in six-dimensional anti-de Sitter space. This set-up has been introduced in the context of brane world models and, higher-dimensional versions of it, in string theory. In both six- and ten-dimensional cases, it has been shown that four-dimensional gravity can be reproduced at the intersection, due to the existence of a massless, localized graviton zero-mode. However, realistic scenarios require also the Standard Model to be localized on the $3-$brane. In this paper, we discuss under which conditions a higher-dimensional field theory, propagating on the above geometry, can have a zero-mode sector localized at the intersection and find that zero modes can be localized only if masses and couplings to the background curvature satisfy certain relations. We also consider the case when other 4-branes cut the bulk at some distance from the intersection and argue that, in the probe brane approximation, there is no significant effect on the localization properties at the $3-$brane. The case of bulk fermions is particularly interesting, since the properties of the geometry allow localization of chiral modes independently.Comment: 13 pages, 3 figures, the version to be published in PR

Cold collisions of heavy 2Σ^2\Sigma molecules with alkali-metal atoms in a magnetic field: Ab initio analysis and prospects for sympathetic cooling of SrOH(2Σ)(^2\Sigma) by Li(2^2S)

We use accurate ab initio and quantum scattering calculations to explore the prospects for sympathetic cooling of the heavy molecular radical SrOH($^2\Sigma$) by ultracold Li atoms in a magnetic trap. A two-dimensional potential energy surface (PES) for the triplet electronic state of Li-SrOH is calculated ab initio using the partially spin-restricted coupled cluster method with single, double and perturbative triple excitations and a large correlation-consistent basis set. The highly anisotropic PES has a deep global minimum in the skewed Li-HOSr geometry with $D_e=4932$ cm$^{-1}$ and saddle points in collinear configurations. Our quantum scattering calculations predict low spin relaxation rates in fully spin-polarized Li+SrOH collisions with the ratios of elastic to inelastic collision rates well in excess of 100 over a wide range of magnetic fields (1-1000 G) and collision energies (10$^{-5}-0.1$~K) suggesting favorable prospects for sympathetic cooling of SrOH molecules with spin-polarized Li atoms in a magnetic trap. We find that spin relaxation in Li+SrOH collisions occurs via a direct mechanism mediated by the magnetic dipole-dipole interaction between the electron spins of Li and SrOH, and that the indirect (spin-rotation) mechanism is strongly suppressed. The upper limit to the Li+SrOH reaction rate coefficient calculated for the singlet PES using adiabatic capture theory is found to decrease from $4\times 10^{-10}$~cm$^3$/s to a limiting value of $3.5\times 10^{-10}$ cm$^3$/s with decreasing temperature from 0.1 K to 1 $\mu$K

Enumeration of bigrassmannian permutations below a permutation in Bruhat order

In theory of Coxeter groups, bigrassmannian elements are well known as elements which have precisely one left descent and precisely one right descent. In this article, we prove formulas on enumeration of bigrassmannian permutations weakly below a permutation in Bruhat order in the symmetric groups. For the proof, we use equivalent characterizations of bigrassmannian permutations by Lascoux-Schutzenberger and Reading.Comment: 7 pages