Unitary Positive-Energy Representations of Scalar Bilocal Quantum Fields

The superselection sectors of two classes of scalar bilocal quantum fields in D>=4 dimensions are explicitly determined by working out the constraints imposed by unitarity. The resulting classification in terms of the dual of the respective gauge groups U(N) and O(N) confirms the expectations based on general results obtained in the framework of local nets in algebraic quantum field theory, but the approach using standard Lie algebra methods rather than abstract duality theory is complementary. The result indicates that one does not lose interesting models if one postulates the absence of scalar fields of dimension D-2 in models with global conformal invariance. Another remarkable outcome is the observation that, with an appropriate choice of the Hamiltonian, a Lie algebra embedded into the associative algebra of observables completely fixes the representation theory.Comment: 27 pages, v3: result improved by eliminating redundant assumptio

Infinite dimensional Lie algebras in 4D conformal quantum field theory

The concept of global conformal invariance (GCI) opens the way of applying algebraic techniques, developed in the context of 2-dimensional chiral conformal field theory, to a higher (even) dimensional space-time. In particular, a system of GCI scalar fields of conformal dimension two gives rise to a Lie algebra of harmonic bilocal fields, V_m(x,y), where the m span a finite dimensional real matrix algebra M closed under transposition. The associative algebra M is irreducible iff its commutant M' coincides with one of the three real division rings. The Lie algebra of (the modes of) the bilocal fields is in each case an infinite dimensional Lie algebra: a central extension of sp(infty,R) corresponding to the field R of reals, of u(infty,infty) associated to the field C of complex numbers, and of so*(4 infty) related to the algebra H of quaternions. They give rise to quantum field theory models with superselection sectors governed by the (global) gauge groups O(N), U(N), and U(N,H)=Sp(2N), respectively.Comment: 16 pages, with minor improvements as to appear in J. Phys.

Supplementary materials for: Variable slip mode in the past 3300 years on the fault ruptured in the 2012 M 5.6 Pernik slow earthquake in Bulgaria

Supplementary materials for the paper Variable slip mode in the past 3300 years on the fault ruptured in the 2012 M 5.6 Pernik slow earthquake in Bulgaria submitted to Natural Hazards. The Supplementary materials contain high-resolution photomosaics of the trench excavated on the Meshtitsa fault, a X-ray diffractogram, locations of the ground cracks observed after the 2012 Pernik earthquake in a Keyhole Markup Language (KML) file format, and resistivity data collected across the Meshtitsa fault scarp in the format used by the Boundless Electrical Resistivity Tomography (BERT) software

Optical to near-infrared transmission spectrum of the warm sub-Saturn HAT-P-12b

We present the transmission spectrum of HAT-P-12b through a joint analysis of data obtained from the Hubble Space Telescope Space Telescope Imaging Spectrograph (STIS) and Wide Field Camera 3 (WFC3) and Spitzer, covering the wavelength range 0.3-5.0 $\mu$m. We detect a muted water vapor absorption feature at 1.4 $\mu$m attenuated by clouds, as well as a Rayleigh scattering slope in the optical indicative of small particles. We interpret the transmission spectrum using both the state-of-the-art atmospheric retrieval code SCARLET and the aerosol microphysics model CARMA. These models indicate that the atmosphere of HAT-P-12b is consistent with a broad range of metallicities between several tens to a few hundred times solar, a roughly solar C/O ratio, and moderately efficient vertical mixing. Cloud models that include condensate clouds do not readily generate the sub-micron particles necessary to reproduce the observed Rayleigh scattering slope, while models that incorporate photochemical hazes composed of soot or tholins are able to match the full transmission spectrum. From a complementary analysis of secondary eclipses by Spitzer, we obtain measured depths of $0.042\%\pm0.013\%$ and $0.045\%\pm0.018\%$ at 3.6 and 4.5 $\mu$m, respectively, which are consistent with a blackbody temperature of $890^{+60}_{-70}$ K and indicate efficient day-night heat recirculation. HAT-P-12b joins the growing number of well-characterized warm planets that underscore the importance of clouds and hazes in our understanding of exoplanet atmospheres.Comment: 25 pages, 19 figures, accepted for publication in AJ, updated with proof correction

The Very Low Albedo of WASP-12b From Spectral Eclipse Observations with Hubble\textit{Hubble}

We present an optical eclipse observation of the hot Jupiter WASP-12b using the Space Telescope Imaging Spectrograph on board the Hubble Space Telescope. These spectra allow us to place an upper limit of $A_g < 0.064$ (97.5% confidence level) on the planet's white light geometric albedo across 290--570 nm. Using six wavelength bins across the same wavelength range also produces stringent limits on the geometric albedo for all bins. However, our uncertainties in eclipse depth are $\sim$40% greater than the Poisson limit and may be limited by the intrinsic variability of the Sun-like host star --- the solar luminosity is known to vary at the $10^{-4}$ level on a timescale of minutes. We use our eclipse depth limits to test two previously suggested atmospheric models for this planet: Mie scattering from an aluminum-oxide haze or cloud-free Rayleigh scattering. Our stringent nondetection rules out both models and is consistent with thermal emission plus weak Rayleigh scattering from atomic hydrogen and helium. Our results are in stark contrast with those for the much cooler HD 189733b, the only other hot Jupiter with spectrally resolved reflected light observations; those data showed an increase in albedo with decreasing wavelength. The fact that the first two exoplanets with optical albedo spectra exhibit significant differences demonstrates the importance of spectrally resolved reflected light observations and highlights the great diversity among hot Jupiters.Comment: 8 pages, 4 figures, 1 table, published in ApJL, in pres

Gemini/GMOS Optical Transmission Spectroscopy of WASP-121b: signs of variability in an ultra-hot Jupiter?

We present ground-based, spectroscopic observations of two transits of the ultra-hot Jupiter WASP-121b covering the wavelength range $\approx$500 - 950 nm using Gemini/GMOS. We use a Gaussian process framework to model instrumental systematics in the light curves, and also demonstrate the use of the more generalised Student's-T process to verify our results. We find that our measured transmission spectrum, whilst showing overall agreement, is slightly discrepant with results obtained using HST/STIS, particularly for wavelengths shortward of $\approx$650 nm. In contrast to the STIS results, we find evidence for an increasing blueward slope and little evidence for absorption from either TiO or VO in our retrieval, in agreement with a number of recent studies performed at high-resolution. We suggest that this might point to some other absorbers, particularly some combination of recently detected atomic metals, in addition to scattering by hazes, being responsible for the excess optical absorption and observed vertical thermal inversion. Our results are also broadly consistent with previous ground-based photometry and 3D GCM predictions, however, these assumed different chemistry to our retrievals. In addition, we show that the GMOS observations are repeatable over short periods (days), similarly to the HST/STIS observations. Their difference over longer periods (months) could well be the result of temporal variability in the atmospheric properties (i.e. weather) as predicted by theoretical models of ultra-hot Jupiters; however, more mundane explanations such as instrumental systematics and stellar activity cannot be fully ruled out, and we encourage future observations to explore this possibility.Comment: 17 pages, 10 Figures. Accepted for publication in MNRA

On Conformal Infinity and Compactifications of the Minkowski Space

Using the standard Cayley transform and elementary tools it is reiterated that the conformal compactification of the Minkowski space involves not only the "cone at infinity" but also the 2-sphere that is at the base of this cone. We represent this 2-sphere by two additionally marked points on the Penrose diagram for the compactified Minkowski space. Lacks and omissions in the existing literature are described, Penrose diagrams are derived for both, simple compactification and its double covering space, which is discussed in some detail using both the U(2) approach and the exterior and Clifford algebra methods. Using the Hodge * operator twistors (i.e. vectors of the pseudo-Hermitian space H_{2,2}) are realized as spinors (i.e., vectors of a faithful irreducible representation of the even Clifford algebra) for the conformal group SO(4,2)/Z_2. Killing vector fields corresponding to the left action of U(2) on itself are explicitly calculated. Isotropic cones and corresponding projective quadrics in H_{p,q} are also discussed. Applications to flat conformal structures, including the normal Cartan connection and conformal development has been discussed in some detail.Comment: 38 pages, 8 figures, late

Radial velocity eclipse mapping of exoplanets

Planetary rotation rates and obliquities provide information regarding the history of planet formation, but have not yet been measured for evolved extrasolar planets. Here we investigate the theoretical and observational perspective of the Rossiter-McLauglin effect during secondary eclipse (RMse) ingress and egress for transiting exoplanets. Near secondary eclipse, when the planet passes behind the parent star, the star sequentially obscures light from the approaching and receding parts of the rotating planetary surface. The temporal block of light emerging from the approaching (blue-shifted) or receding (red-shifted) parts of the planet causes a temporal distortion in the planet's spectral line profiles resulting in an anomaly in the planet's radial velocity curve. We demonstrate that the shape and the ratio of the ingress-to-egress radial velocity amplitudes depends on the planetary rotational rate, axial tilt and impact factor (i.e. sky-projected planet spin-orbital alignment). In addition, line asymmetries originating from different layers in the atmosphere of the planet could provide information regarding zonal atmospheric winds and constraints on the hot spot shape for giant irradiated exoplanets. The effect is expected to be most-pronounced at near-infrared wavelengths, where the planet-to-star contrasts are large. We create synthetic near-infrared, high-dispersion spectroscopic data and demonstrate how the sky-projected spin axis orientation and equatorial velocity of the planet can be estimated. We conclude that the RMse effect could be a powerful method to measure exoplanet spins.Comment: 7 pages, 3 figures, 1 table, accepted for publication in ApJ on 2015 June 1