On the 2D zero modes' algebra of the SU(n) WZNW model

A quantum group covariant extension of the chiral parts of the Wess-Zumino-Novikov-Witten model on a compact Lie group G gives rise to two matrix algebras with non-commutative entries. These are generated by "chiral zero modes" which combine in the 2D model into "Q-operators" which encode information about the internal symmetry and the fusion ring. We review earlier results about the SU(n) WZNW Q-algebra and its Fock representation for n=2 and display the first steps towards their generalization to higher n.Comment: 10 pages, Talk presented by L.H. at the International Workshop LT10 (17-23 June 2013, Varna, Bulgaria

The Densities of Planets in Multiple Stellar Systems

We analyze the effect of companion stars on the bulk density of 29 planets orbiting 15 stars in the Kepler field. These stars have at least one stellar companion within 2", and the planets have measured masses and radii, allowing an estimate of their bulk density. The transit dilution by the companion star requires the planet radii to be revised upward, even if the planet orbits the primary star; as a consequence, the planetary bulk density decreases. We find that, if planets orbited a faint companion star, they would be more volatile-rich, and in several cases their densities would become unrealistically low, requiring large, inflated atmospheres or unusually large mass fractions in a H/He envelope. In addition, for planets detected in radial velocity data, the primary star has to be the host. We can exclude 14 planets from orbiting the companion star; the remaining 15 planets in seven planetary systems could orbit either the primary or the secondary star, and for five of these planets the decrease in density would be substantial even if they orbited the primary, since the companion is of almost equal brightness as the primary. Substantial follow-up work is required in order to accurately determine the radii of transiting planets. Of particular interest are small, rocky planets that may be habitable; a lower mean density might imply a more volatile-rich composition. Reliable radii, masses, and thus bulk densities will allow us to identify which small planets are truly Earth-like.Comment: Accepted by AJ; 22 page

The VLA/ALMA Nascent Disk and Multiplicity (VANDAM) Survey of Orion Protostars. II. A Statistical Characterization of Class 0 and Class I Protostellar Disks

We have conducted a survey of 328 protostars in the Orion molecular clouds with the Atacama Large Millimeter/submillimeter Array at 0.87 mm at a resolution of ~0.”1 (40 au), including observations with the Very Large Array at 9 mm toward 148 protostars at a resolution of ~0 08 (32 au). This is the largest multiwavelength survey of protostars at this resolution by an order of magnitude. We use the dust continuum emission at 0.87 and 9 mm to measure the dust disk radii and masses toward the Class 0, Class I, and flat-spectrum protostars, characterizing the evolution of these disk properties in the protostellar phase. The mean dust disk radii for the Class 0, Class I, and flat-spectrum protostars are 44.9^(+5.8)_(−3.4), 37.0^(+4.9)_(−3.0), and 28.5^(+3.7)_(−2.3) au, respectively, and the mean protostellar dust disk masses are 25.9^(+7.7)_(−4.0), 14.9^(+3.8)_(−2.2), 1.6^(+3.5)_(−1.9) M⊕, respectively. The decrease in dust disk masses is expected from disk evolution and accretion, but the decrease in disk radii may point to the initial conditions of star formation not leading to the systematic growth of disk radii or that radial drift is keeping the dust disk sizes small. At least 146 protostellar disks (35% of 379 detected 0.87 mm continuum sources plus 42 nondetections) have disk radii greater than 50 au in our sample. These properties are not found to vary significantly between different regions within Orion. The protostellar dust disk mass distributions are systematically larger than those of Class II disks by a factor of >4, providing evidence that the cores of giant planets may need to at least begin their formation during the protostellar phase

Fusion rules for admissible representations of affine algebras: the case of A2(1)A_2^{(1)}

We derive the fusion rules for a basic series of admissible representations of $\hat{sl}(3)$ at fractional level $3/p-3$. The formulae admit an interpretation in terms of the affine Weyl group introduced by Kac and Wakimoto. It replaces the ordinary affine Weyl group in the analogous formula for the fusion rules multiplicities of integrable representations. Elements of the representation theory of a hidden finite dimensional graded algebra behind the admissible representations are briefly discussed.Comment: containing two TEX files: main file using input files harvmac.tex, amssym.def, amssym.tex, 19p.; file with figures using XY-pic package, 6p. Correction in the definition of general shifted weight diagra

A Higgs Conundrum with Vector Fermions

Many models of Beyond the Standard Model physics involve heavy colored fermions. We study models where the new fermions have vector interactions and examine the connection between electroweak precision measurements and Higgs production. In particular, for parameters which are allowed by precision measurements, we show that the gluon fusion Higgs cross section and the Higgs decay branching ratios must be close to those predicted by the Standard Model. The models we discuss thus represent scenarios with new physics which will be extremely difficult to distinguish from the minimal Standard Model. We pay particular attention to the decoupling properties of the vector fermions.Comment: 34 pages, 15 figures. Version accepted for publication in Phys. Rev.