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.

Large-scale Hierarchical Alignment for Data-driven Text Rewriting

We propose a simple unsupervised method for extracting pseudo-parallel monolingual sentence pairs from comparable corpora representative of two different text styles, such as news articles and scientific papers. Our approach does not require a seed parallel corpus, but instead relies solely on hierarchical search over pre-trained embeddings of documents and sentences. We demonstrate the effectiveness of our method through automatic and extrinsic evaluation on text simplification from the normal to the Simple Wikipedia. We show that pseudo-parallel sentences extracted with our method not only supplement existing parallel data, but can even lead to competitive performance on their own.Comment: RANLP 201

Character-level Chinese-English Translation through ASCII Encoding

Character-level Neural Machine Translation (NMT) models have recently achieved impressive results on many language pairs. They mainly do well for Indo-European language pairs, where the languages share the same writing system. However, for translating between Chinese and English, the gap between the two different writing systems poses a major challenge because of a lack of systematic correspondence between the individual linguistic units. In this paper, we enable character-level NMT for Chinese, by breaking down Chinese characters into linguistic units similar to that of Indo-European languages. We use the Wubi encoding scheme, which preserves the original shape and semantic information of the characters, while also being reversible. We show promising results from training Wubi-based models on the character- and subword-level with recurrent as well as convolutional models.Comment: 7 pages, 3 figures, 3rd Conference on Machine Translation (WMT18), 201

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

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

Refined physical properties and g',r',i',z',J,H,K transmission spectrum of WASP-23b from the ground

Multi-band observations of planetary transits using the telescope defocus technique may yield high-quality light curves suitable for refining the physical properties of exoplanets even with small or medium size telescopes. Such observations can be used to construct a broad-band transmission spectrum of transiting planets and search for the presence of strong absorbers. We have thoroughly characterised the orbital ephemeris and physical properties of the transiting planet and host star in the WASP-23b system, constructed a broad-band transmission spectrum of WASP-23b and performed a comparative analysis with theoretical models of hot Jupiters. We observed a complete transit of WASP-23b in seven bands simultaneously, using the GROND instrument on the MPG/ESO 2.2m telescope at La Silla Observatory and telescope defocussing. The optical data were taken in the Sloan g',r',i' and z' bands. The resulting light curves are of high quality, with a root-mean-square scatter of the residual as low as 330ppm in the z'-band, with a cadence of 90s. Near-infrared data were obtained in the JHK bands. We performed MCMC analysis of our photometry plus existing radial velocity data to refine measurements of the ephemeris and physical properties of the WASP-23. We constructed a broad-band transmission spectrum of WASP-23b and compared it with a theoretical transmission spectrum of a Hot Jupiter. We measured the central transit time with a precision about 8s. From this and earlier observations we obtain an orbital period of P=2.9444300+/-0.0000011d. Our analysis also yielded a larger radius and mass for the planet (Rp=1.067+0.045-0.038 RJup and, Mp=0.917+0.040-0.039MJup). The transmission spectrum is marginally flat, given the limited precision of the measurements for the planet radius and poor spectral resolution of the data.Comment: 8 pages, 5 figures, accepted for publication in Astronomy & Astrophysic

2MASSJ22560844+5954299: the newly discovered cataclysmic star with the deepest eclipse

Context: The SW Sex stars are assumed to represent a distinguished stage in CV evolution, making it especially important to study them. Aims: We discovered a new cataclysmic star and carried out prolonged and precise photometric observations, as well as medium-resolution spectral observations. Modelling these data allowed us to determine the psysical parameters and to establish its peculiarities. Results: The newly discovered vataclysmic variable 2MASSJ22560844+5954299 shows the deepest eclipse amongst the known nova-like stars. It was reproduced by totally covering a very luminous accretion disk by a red secondary component. The temperature distribution of the disk is flatter than that of steady-state disk. The target is unusual with the combination of a low mass ratio q~1.0 (considerably below the limit q=1.2 of stable mass transfer of CVs) and an M-star secondary. The intensity of the observed three emission lines, H_alpha, He 5875, and He 6678, sharply increases around phase 0.0, accompanied by a Doppler jump to the shorter wavelength. The absence of eclipses of the emission lines and their single-peaked profiles means that they originate mainly in a vertically extended hot-spot halo. The emission H_alpha line reveals S-wave wavelength shifts with semi-amplitude of around 210 km/s and phase lag of 0.03. Conclusions: The non-steady-state emission of the luminous accretion disk of 2MASSJ22560844+5954299 was attributed to the low viscosity of the disk matter caused by its unusually high temperature. The star shows all spectral properties of an SW Sex variable apart from the 0.5 central absorption.Comment: Accepted for publication in Astronomy & Astrophysics. 12 pages, 11 figures, 6 table

Entire curves avoiding given sets in C^n

Let $F\subset\Bbb C^n$ be a proper closed subset of $\Bbb C^n$ and $A\subset\Bbb C^n\setminus F$ at most countable ($n\geq 2$). We give conditions of $F$ and $A$, under which there exists a holomorphic immersion (or a proper holomorphic embedding) $\phi:\Bbb C\to\Bbb C^n$ with $A\subset\phi(\Bbb C)\subset\Bbb C^n\setminus F$.Comment: 10 page

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

Physical properties of the WASP-44 planetary system from simultaneous multi-colour photometry

We present ground-based broad-band photometry of two transits in the WASP-44 planetary system obtained simultaneously through four optical (Sloan g', r', i', z') and three near-infrared (NIR; J, H, K) filters. We achieved low scatters of 1-2 mmag per observation in the optical bands with a cadence of 48 s, but the NIR-band light curves present much greater scatter. We also observed another transit of WASP-44 b by using a Gunn-r filter and telescope defocussing, with a scatter of 0.37 mmag per point and an observing cadence around 135 s. We used these data to improve measurements of the time of mid-transit and the physical properties of the system. In particular, we improved the radius measurements of the star and planet by factors of 3 and 4, respectively. We find that the radius of WASP-44 b is 1.002 R_Jup, which is slightly smaller than previously thought and differs from that expected for a core-free planet. In addition, with the help of a synthetic spectrum, we investigated the theoretically-predicted variation of the planetary radius as a function of wavelength, covering the range 370-2440 nm. We can rule out extreme variations at optical wavelengths, but unfortunately our data are not precise enough (especially in the NIR bands) to differentiate between the theoretical spectrum and a radius which does not change with wavelength.Comment: 13 pages, 6 figures, to appear in Monthly Notices of the Royal Astronomical Societ