16,339 research outputs found
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
Fusion rules for admissible representations of affine algebras: the case of
We derive the fusion rules for a basic series of admissible representations
of at fractional level . 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 tightness criterion for random fields, with application to the Ising model
We present a criterion for a family of random distributions to be tight in
local H\"older and Besov spaces of possibly negative regularity. We then apply
this criterion to the magnetization field of the two-dimensional Ising model at
criticality, answering a question of Camia, Garban and Newman.Comment: 28 pages. EJP versio
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.â1 (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)_(â3.4), 37.0^(+4.9)_(â3.0), and 28.5^(+3.7)_(â2.3) au, respectively, and the mean protostellar dust disk masses are 25.9^(+7.7)_(â4.0), 14.9^(+3.8)_(â2.2), 1.6^(+3.5)_(â1.9) Mâ, 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
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
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