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.

Physical properties, starspot activity, orbital obliquity, and transmission spectrum of the Qatar-2 planetary system from multi-colour photometry

We present seventeen high-precision light curves of five transits of the planet Qatar-2b, obtained from four defocussed 2m-class telescopes. Three of the transits were observed simultaneously in the SDSS griz passbands using the seven-beam GROND imager on the MPG/ESO 2.2-m telescope. A fourth was observed simultaneously in Gunn grz using the CAHA 2.2-m telescope with BUSCA, and in r using the Cassini 1.52-m telescope. Every light curve shows small anomalies due to the passage of the planetary shadow over a cool spot on the surface of the host star. We fit the light curves with the prism+gemc model to obtain the photometric parameters of the system and the position, size and contrast of each spot. We use these photometric parameters and published spectroscopic measurements to obtain the physical properties of the system to high precision, finding a larger radius and lower density for both star and planet than previously thought. By tracking the change in position of one starspot between two transit observations we measure the orbital obliquity of Qatar-2 b to be 4.3 \pm 4.5 degree, strongly indicating an alignment of the stellar spin with the orbit of the planet. We calculate the rotation period and velocity of the cool host star to be 11.4 \pm 0.5 d and 3.28 \pm 0.13 km/s at a colatitude of 74 degree. We assemble the planet's transmission spectrum over the 386-976 nm wavelength range and search for variations of the measured radius of Qatar-2 b as a function of wavelength. Our analysis highlights a possible H2/He Rayleigh scattering in the blue.Comment: 20 pages, 14 figures, to appear in Monthly Notices of the Royal Astronomical Societ

Jacobi Identity for Vertex Algebras in Higher Dimensions

Vertex algebras in higher dimensions provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance. We develop further the theory of such vertex algebras by introducing formal calculus techniques and investigating the notion of polylocal fields. We derive a Jacobi identity which together with the vacuum axiom can be taken as an equivalent definition of vertex algebra.Comment: 35 pages, references adde

Simultaneous follow-up of planetary transits: revised physical properties for the planetary systems HAT-P-16 and WASP-21

Context. By now more than 300 planets transiting their host star have been found, and much effort is being put into measuring the properties of each system. Light curves of planetary transits often contain deviations from a simple transit shape, and it is generally difficult to differentiate between anomalies of astrophysical nature (e.g. starspots) and correlated noise due to instrumental or atmospheric effects. Our solution is to observe transit events simultaneously with two telescopes located at different observatories. Aims. Using this observational strategy, we look for anomalies in the light curves of two transiting planetary systems and accurately estimate their physical parameters. Methods. We present the first photometric follow-up of the transiting planet HAT-P-16 b, and new photometric observations of WASP-21 b, obtained simultaneously with two medium-class telescopes located in different countries, using the telescope defocussing technique. We modeled these and other published data in order to estimate the physical parameters of the two planetary systems. Results. The simultaneous observations did not highlight particular features in the light curves, which is consistent with the low activity levels of the two stars. For HAT-P-16, we calculated a new ephemeris and found that the planet is 1.3 \sigma colder and smaller (Rb = 1.190 \pm 0.037 RJup) than the initial estimates, suggesting the presence of a massive core. Our physical parameters for this system point towards a younger age than previously thought. The results obtained for WASP-21 reveal lower values for the mass and the density of the planet (by 1.0 \sigma and 1.4 \sigma respectively) with respect to those found in the discovery paper, in agreement with a subsequent study. We found no evidence of any transit timing variations in either system.Comment: 8 pages, 6 figures, accepted for publication in A&

HATS-5b: A Transiting hot-Saturn from the HATSouth Survey

We report the discovery of HATS-5b, a transiting hot-Saturn orbiting a G type star, by the HAT-South survey. HATS-5b has a mass of Mp=0.24 Mj, radius of Rp=0.91 Rj, and transits its host star with a period of P=4.7634d. The radius of HATS-5b is consistent with both theoretical and empirical models. The host star has a V band magnitude of 12.6, mass of 0.94 Msun, and radius of 0.87 Rsun. The relatively high scale height of HATS-5b, and the bright, photometrically quiet host star, make this planet a favourable target for future transmission spectroscopy follow-up observations. We reexamine the correlations in radius, equilibrium temperature, and metallicity of the close-in gas-giants, and find hot Jupiter-mass planets to exhibit the strongest dependence between radius and equilibrium temperature. We find no significant dependence in radius and metallicity for the close-in gas-giant population.Comment: 10 pages, submitted to A