Sharpenings of Li's criterion for the Riemann Hypothesis

Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. For $n \to \infty$ we obtain that if (and only if) the Hypothesis is true, $\lambda_n \sim n(A \log n +B)$ (with $A>0$ and $B$ explicitly given, also for the case of more general zeta or $L$-functions); whereas in the opposite case, $\lambda_n$ has a non-tempered oscillatory form.Comment: 10 pages, Math. Phys. Anal. Geom (2006, at press). V2: minor text corrections and updated reference

On effective actions of BPS branes and their higher derivative corrections

We calculate in detail the disk level S-matrix element of one Ramond-Ramond field and three gauge field vertex operators in the world volume of BPS branes, to find four gauge field couplings to all orders of $\alpha'$ up to on-shell ambiguity. Then using these infinite couplings we find that the massless pole of the field theory amplitude is exactly equal to the massless pole S-matrix element of this amplitude for the $p=n$ case to all orders of $\alpha'$. Finally we show that the infinite massless poles and the contact terms of this amplitude for the $p=n+2$ case can be reproduced by the Born-Infeld action and the Wess-Zumino actions and by their higher derivative corrections.Comment: 26 pages, 2 figures, minor corrections,references added and version published in JHE

Cosmological anti-deSitter space-times and time-dependent AdS/CFT correspondence

We study classes of five-dimensional cosmological solutions with negative curvature, which are obtained from static solutions by an exchange of a spatial and temporal coordinate, and in some cases by an analytic continuation. Such solutions provide a suitable laboratory to address the time-dependent AdS/CFT correspondence. For a specific example we address in detail the calculation of the boundary stress-energy and the Wilson line and find disagreement with the standard AdS/CFT correspondence. We trace these discrepancies to the time-dependent effects, such as particle creation, which we further study for specific backgrounds. We also identify specific time-dependent backgrounds that reproduce the correct conformal anomaly. For such backgrounds the calculation of the Wilson line in the adiabatic approximation indicates only a Coulomb repulsion.Comment: LaTeX file, 47 pages, discussion is extended, version to appear in PR

Symmetry breaking orbital anisotropy on detwinned Ba(Fe1-xCox)2As2 above the spin density wave transition

Nematicity, defined as broken rotational symmetry, has recently been observed in competing phases proximate to the superconducting phase in the cuprate high temperature superconductors. Similarly, the new iron-based high temperature superconductors exhibit a tetragonal to orthorhombic structural transition (i.e. a broken C4 symmetry) that either precedes or is coincident with a collinear spin density wave (SDW) transition in undoped parent compounds, and superconductivity arises when both transitions are suppressed via doping. Evidence for strong in-plane anisotropy in the SDW state in this family of compounds has been reported by neutron scattering, scanning tunneling microscopy, and transport measurements. Here we present an angle resolved photoemission spectroscopy study of detwinned single crystals of a representative family of electron-doped iron-arsenide superconductors, Ba(Fe1-xCox)2As2 in the underdoped region. The crystals were detwinned via application of in-plane uniaxial stress, enabling measurements of single domain electronic structure in the orthorhombic state. At low temperatures, our results clearly demonstrate an in-plane electronic anisotropy characterized by a large energy splitting of two orthogonal bands with dominant dxz and dyz character, which is consistent with anisotropy observed by other probes. For compositions x>0, for which the structural transition (TS) precedes the magnetic transition (TSDW), an anisotropic splitting is observed to develop above TSDW, indicating that it is specifically associated with TS. For unstressed crystals, the band splitting is observed close to TS, whereas for stressed crystals the splitting is observed to considerably higher temperatures, revealing the presence of a surprisingly large in-plane nematic susceptibility in the electronic structure.Comment: final version published in PNAS, including supplementary informatio

Strong-coupling Spin-singlet Superconductivity with Multiple Full Gaps in Hole-doped Ba0.6_{0.6}K0.4_{0.4}Fe2_2As2_2 Probed by Fe-NMR

We present $^{57}$Fe-NMR measurements of the novel normal and superconducting-state characteristics of the iron-arsenide superconductor Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ ($T_c$ = 38 K). In the normal state, the measured Knight shift and nuclear spin-lattice relaxation rate $(1/T_1)$ demonstrate the development of wave-number ($q$)-dependent spin fluctuations, except at $q$ = 0, which may originate from the nesting across the disconnected Fermi surfaces. In the superconducting state, the spin component in the $^{57}$Fe-Knight shift decreases to almost zero at low temperatures, evidencing a spin-singlet superconducting state. The $^{57}$Fe-$1/T_1$ results are totally consistent with a $s^\pm$-wave model with multiple full gaps, regardless of doping with either electrons or holes.Comment: 4 pages, 4 figures, 1 tabl

Non-Equilibrium Field Dynamics of an Honest Holographic Superconductor

Most holographic models of superconducting systems neglect the effects of dynamical boundary gauge fields during the process of spontaneous symmetry-breaking. Usually a global symmetry gets broken. This yields a superfluid, which then is gauged "weakly" afterwards. In this work we build (and probe the dynamics of) a holographic model in which a local boundary symmetry is spontaneously broken instead. We compute two-point functions of dynamical non-Abelian gauge fields in the normal and in the broken phase, and find non-trivial gapless modes. Our AdS3 gravity dual realizes a p-wave superconductor in (1+1) dimensions. The ground state of this model also breaks (1+1)-dimensional parity spontaneously, while the Hamiltonian is parity-invariant. We discuss possible implications of our results for a wider class of holographic liquids.Comment: 32 pages, 12 figures; v3: string theory derivation of setup added (section 3.1), improved presentation, version accepted by JHEP; v2: paragraph added to discussion, figure added, references added, typos correcte

Determining the extragalactic extinction law with SALT

We present CCD imaging observations of early-type galaxies with dark lanes obtained with the Southern African Large Telescope (SALT) during its performance-verification phase. We derive the extinction law by the extragalactic dust in the dark lanes in the spectral range 1.11mu m^{-1} < lambda^{-1} < 2.94 mu m^{-1} by fitting model galaxies to the unextinguished parts of the image, and subtracting from these the actual images. We find that the extinction curves run parallel to the Galactic extinction curve, which implies that the properties of dust in the extragalactic enviroment are similar to those of the Milky Way. The ratio of the total V band extinction to the selective extinction between the V and B bands is derived for each galaxy with an average of 2.82+-0.38, compared to a canonical value of 3.1 for the Milky Way. The similar values imply that galaxies with well-defined dark lanes have characteristic dust grain sizes similar to those of Galactic dust.Comment: 20 pages, 15 figures and 4 tables. Accepted for publication in MNRA

A Unified Description of Cuprate and Iron Arsenide Superconductors

We propose a unified description of cuprate and iron-based superconductivity. Consistency with magnetic structure inferred from neutron scattering implies significant constraints on the symmetry of the pairing gap for the iron-based superconductors. We find that this unification requires the orbital pairing formfactors for the iron arsenides to differ fundamentally from those for cuprates at the microscopic level.Comment: 12 pages, 10 figures, 2 table