Eisenstein Series and String Thresholds

We investigate the relevance of Eisenstein series for representing certain $G(Z)$-invariant string theory amplitudes which receive corrections from BPS states only. $G(Z)$ may stand for any of the mapping class, T-duality and U-duality groups $Sl(d,Z)$, $SO(d,d,Z)$ or $E_{d+1(d+1)}(Z)$ respectively. Using $G(Z)$-invariant mass formulae, we construct invariant modular functions on the symmetric space $K\backslash G(R)$ of non-compact type, with $K$ the maximal compact subgroup of $G(R)$, that generalize the standard non-holomorphic Eisenstein series arising in harmonic analysis on the fundamental domain of the Poincar\'e upper half-plane. Comparing the asymptotics and eigenvalues of the Eisenstein series under second order differential operators with quantities arising in one- and $g$-loop string amplitudes, we obtain a manifestly T-duality invariant representation of the latter, conjecture their non-perturbative U-duality invariant extension, and analyze the resulting non-perturbative effects. This includes the $R^4$ and $R^4 H^{4g-4}$ couplings in toroidal compactifications of M-theory to any dimension $D\geq 4$ and $D\geq 6$ respectively.Comment: Latex2e, 60 pages; v2: Appendix A.4 extended, 2 refs added, thms renumbered, plus minor corrections; v3: relation (1.7) to math Eis series clarified, eq (3.3) and minor typos corrected, final version to appear in Comm. Math. Phys; v4: misprints and Eq C.13,C.24 corrected, see note adde

On the dimensional dependence of duality groups for massive p-forms

We study the soldering formalism in the context of abelian p-form theories. We develop further the fusion process of massless antisymmetric tensors of different ranks into a massive p-form and establish its duality properties. To illustrate the formalism we consider two situations. First the soldering mass generation mechanism is compared with the Higgs and Julia-Toulouse mechanisms for mass generation due to condensation of electric and magnetic topological defects. We show that the soldering mechanism interpolates between them for even dimensional spacetimes, in this way confirming the Higgs/Julia-Toulouse duality proposed by Quevedo and Trugenberger \cite{QT} a few years ago. Next, soldering is applied to the study of duality group classification of the massive forms. We show a dichotomy controlled by the parity of the operator defining the symplectic structure of the theory and find their explicit actions.Comment: Reference [8] has been properly place

General CMB and Primordial Bispectrum Estimation I: Mode Expansion, Map-Making and Measures of f_NL

We present a detailed implementation of two bispectrum estimation methods which can be applied to general non-separable primordial and CMB bispectra. The method exploits bispectrum mode decompositions on the domain of allowed wavenumber or multipole values. Concrete mode examples constructed from symmetrised tetrahedral polynomials are given, demonstrating rapid convergence for known bispectra. We use these modes to generate simulated CMB maps of high resolution (l > 2000) given an arbitrary primordial power spectrum and bispectrum or an arbitrary late-time CMB angular power spectrum and bispectrum. By extracting coefficients for the same separable basis functions from an observational map, we are able to present an efficient and general f_NL estimator for a given theoretical model. The estimator has two versions comparing theoretical and observed coefficients at either primordial or late times, thus encompassing a wider range of models, including secondary anisotropies, lensing and cosmic strings. We provide examples and validation of both f_NL estimation methods by direct comparison with simulations in a WMAP-realistic context. In addition, we show how the full bispectrum can be extracted from observational maps using these mode expansions, irrespective of the theoretical model under study. We also propose a universal definition of the bispectrum parameter F_NL for more consistent comparison between theoretical models. We obtain WMAP5 estimates of f_NL for the equilateral model from both our primordial and late-time estimators which are consistent with each other, as well as with results already published in the literature. These general bispectrum estimation methods should prove useful for the analysis of nonGaussianity in the Planck satellite data, as well as in other contexts.Comment: 41 pages, 17 figure

Topological insulator particles as optically induced oscillators: towards dynamical force measurements and optical rheology

We report the first experimental study upon the optical trapping and manipulation of topological insulator (TI) particles. By virtue of the unique TI properties, which have a conducting surface and an insulating bulk, the particles present a peculiar behaviour in the presence of a single laser beam optical tweezers: they oscillate in a plane perpendicular to the direction of the laser propagation, as a result of the competition between radiation pressure and gradient forces. In other words, TI particles behave as optically induced oscillators, allowing dynamical measurements with unprecedented simplicity and purely optical control. Actually, optical rheology of soft matter interfaces and biological membranes, as well as dynamical force measurements in macromolecules and biopolymers, may be quoted as feasible possibilities for the near future.Comment: 6 pages, 5 figures. Correspondence and requests for Supplementary Material should be addressed to [email protected]

Black string corrections in variable tension braneworld scenarios

Braneworld models with variable tension are investigated, and the corrections on the black string horizon along the extra dimension are provided. Such corrections are encrypted in additional terms involving the covariant derivatives of the variable tension on the brane, providing profound consequences concerning the black string horizon variation along the extra dimension, near the brane. The black string horizon behavior is shown to be drastically modified by the terms corrected by the brane variable tension. In particular, a model motivated by the phenomenological interesting case regarding Eotvos branes is investigated. It forthwith provides further physical features regarding variable tension braneworld scenarios, heretofore concealed in all previous analysis in the literature. All precedent analysis considered uniquely the expansion of the metric up to the second order along the extra dimension, what is able to evince solely the brane variable tension absolute value. Notwithstanding, the expansion terms aftermath, further accomplished in this paper from the third order on, elicits the successive covariant derivatives of the brane variable tension, and their respective coupling with the extrinsic curvature, the Weyl tensor, and the Riemann and Ricci tensors, as well as the scalar curvature. Such additional terms are shown to provide sudden modifications in the black string horizon in a variable tension braneworld scenarioComment: 12 pages, 5 figures, accepted in PR

Tuning the electrical conductivity of nanotube-encapsulated metallocene wires

We analyze a new family of carbon nanotube-based molecular wires, formed by encapsulating metallocene molecules inside the nanotubes. Our simulations, that are based on a combination of non-equilibrium Green function techniques and density functional theory, indicate that these wires can be engineered to exhibit desirable magnetotransport effects for use in spintronics devices. The proposed structures should also be resilient to room-temperature fluctuations, and are expected to have a high yield.Comment: 4 pages, 6 figures. Accepted in Physical Review Letter

The distance to the LMC cluster NGC 1866 and the surrounding field

We use the Main Sequence stars in the LMC cluster NGC 1866 and of Red Clump stars in the local field to obtain two independent estimates of the LMC distance. We apply an empirical Main Sequence-fitting technique based on a large sample of subdwarfs with accurate {\sl Hipparcos} parallaxes in order to estimate the cluster distance modulus, and the multicolor Red Clump method to derive distance and reddening of the LMC field. We find that the Main Sequence-fitting and the Red Clump distance moduli are in significant disagreement; NGC 1866 distance is equal to $\rm (m-M)_{0,NGC 1866}=18.33\pm$0.08 (consistent with a previous estimate using the same data and theoretical Main Sequence isochrones), while the field stars provide $\rm (m-M)_{0,field}=18.53\pm$0.07. This difference reflects the more general dichotomy in the LMC distance estimates found in the literature. Various possible causes for this disagreement are explored, with particular attention paid to the still uncertain metallicity of the cluster and the star formation history of the field stars.Comment: 5 pages, incl. 1 figure, uses emulateapj.sty, ApJ accepte

Upper bound for the conductivity of nanotube networks

Films composed of nanotube networks have their conductivities regulated by the junction resistances formed between tubes. Conductivity values are enhanced by lower junction resistances but should reach a maximum that is limited by the network morphology. By considering ideal ballistic-like contacts between nanotubes we use the Kubo formalism to calculate the upper bound for the conductivity of such films and show how it depends on the nanotube concentration as well as on their aspect ratio. Highest measured conductivities reported so far are approaching this limiting value, suggesting that further progress lies with nanowires other than nanotubes.Comment: 3 pages, 1 figure. Minor changes. Accepted for publication in Applied Physics Letter