Combinatorial realizations of crystals via torus actions on quiver varieties

Consider Kashiwara's crystal associated to a highest weight representation of a symmetric Kac-Moody algebra. There is a geometric realization of this object using Nakajima's quiver varieties, but in many particular cases it can also be realized by elementary combinatorial methods. Here we propose a framework for extracting combinatorial realizations from the geometric picture: We construct certain torus actions on the quiver varieties and use Morse theory to index the irreducible components by connected components of the subvariety of torus fixed points. We then discuss the case of affine sl(n). There the fixed point components are just points, and are naturally indexed by multi-partitions. There is some choice in our construction, leading to a family of combinatorial models for each highest weight crystal. Applying this construction to the crystal of the fundamental representation recovers a family of combinatorial realizations recently constructed by Fayers. This gives a more conceptual proof of Fayers' result as well as a generalization to higher level. We also discuss a relationship with Nakajima's monomial crystal.Comment: 23 pages, v2: added Section 8 on monomial crystals and some references; v3: many small correction

Infrared Features of the Landau Gauge QCD

The infrared features of Landau gauge QCD are studied by the lattice simulation of $\beta=6.0, 16^4, 24^4, 32^4$ and $\beta=6.4, 32^4, 48^4$. We adopt two definitions of the gauge field; 1) $U-$linear 2) $\log U$ and measured the gluon propagator and ghost propagator. Infrared singularity of the gluon propagator is less than that of tree level result but the gluon propagator at 0 momentum remains finite. The infrared singularity of ghost propagator is stronger than the tree level. The QCD running coupling measured by using the gluon propagator and the ghost propagator has a maximum $\alpha_s(p)\simeq 1$ at around $p=0.5GeV$ and decreases as $p$ approaches 0. The data are analyzed in use of formula of the principle of minimal sensitivity(PMS), the effective charge method and the contour-improved perturbation method, which suggest necessity of the resummation of perturbation series in the infrared region together with existence of the infrared fixed point. Kugo-Ojima parameter saturates at about -0.8 in contrast to the theoretically expected value -1.Comment: RevTex4, 9 pages, 10 eps figures, Typos corrected. To be published in Phys. Rev. D(2004

Vacuum entanglement governs the bosonic character of magnons

It is well known that magnons, elementary excitations in a magnetic material, behave as bosons when their density is low. We study how the bosonic character of magnons is governed by the amount of a multipartite entanglement in the vacuum state on which magnons are excited. We show that if the multipartite entanglement is strong, magnons cease to be bosons. We also consider some examples, such as ground states of the Heisenberg ferromagnet and the transverse Ising model, the condensation of magnons, the one-way quantum computer, and Kitaev's toric code. Our result provides insights into the quantum statistics of elementary excitations in these models, and into the reason why a non-local transformation, such as the Jordan-Wigner transformation, is necessary for some many-body systems.Comment: 4 pages, no figur

Intense CIII] 1907,1909 emission from a strong Lyman continuum emitting galaxy

We have obtained the first complete ultraviolet (UV) spectrum of a strong Lyman continuum(LyC) emitter at low redshift -- the compact, low-metallicity, star-forming galaxy J1154+2443 -- with a Lyman continuum escape fraction of 46% discovered recently. The Space Telescope Imaging Spectrograph spectrum shows strong Lya and CIII] 1909 emission, as well as OIII] 1666. Our observations show that strong LyC emitters can have UV emission lines with a high equivalent width (e.g. EW(CIII])$=11.7 \pm 2.9 \AA$ rest-frame), although their equivalent widths should be reduced due to the loss of ionizing photons. The intrinsic ionizing photon production efficiency of J1154+2443 is high, $\log(\xi_{\rm ion}^0)=25.56$ erg$^{-1}$ Hz, comparable to that of other recently discovered $z \sim 0.3-0.4$ LyC emitters. Combining our measurements and earlier determinations from the literature, we find a trend of increasing $\xi_{\rm ion}^0$ with increasing CIII] 1909 equivalent width, which can be understood by a combination of decreasing stellar population age and metallicity. Simple ionization and density-bounded photoionization models can explain the main observational features including the UV spectrum of J1154+2443.Comment: 5 pages, 4 figures. Accepted for publication in A&A Letter

On practical problems to compute the ghost propagator in SU(2) lattice gauge theory

In SU(2) lattice pure gauge theory we study numerically the dependence of the ghost propagator G(p) on the choice of Gribov copies in Lorentz (or Landau) gauge. We find that the effect of Gribov copies is essential in the scaling window region, however, it tends to decrease with increasing beta. On the other hand, we find that at larger beta-values very strong fluctuations appear which can make problematic the calculation of the ghost propagator.Comment: 15 pages, 5 postscript figures. 2 Figures added Revised version as to be published in Phys.Rev.

Instantons on ALE spaces and Super Liouville Conformal Field Theories

We provide evidence that the conformal blocks of N=1 super Liouville conformal field theory are described in terms of the SU(2) Nekrasov partition function on the ALE space O_{P^1}(-2).Comment: 10 page

A crystal theoretic method for finding rigged configurations from paths

The Kerov--Kirillov--Reshetikhin (KKR) bijection gives one to one correspondences between the set of highest paths and the set of rigged configurations. In this paper, we give a crystal theoretic reformulation of the KKR map from the paths to rigged configurations, using the combinatorial R and energy functions. This formalism provides tool for analysis of the periodic box-ball systems.Comment: 24 pages, version for publicatio

Broadband microwave burst produced by electron beams

Theoretical and experimental study of fast electron beams attracts a lot of attention in the astrophysics and laboratory. In the case of solar flares the problem of reliable beam detection and diagnostics is of exceptional importance. This paper explores the fact that the electron beams moving oblique to the magnetic field or along the field with some angular scatter around the beam propagation direction can generate microwave continuum bursts via gyrosynchrotron mechanism. The characteristics of the microwave bursts produced by beams differ from those in case of isotropic or loss-cone distributions, which suggests a new tool for quantitative diagnostics of the beams in the solar corona. To demonstrate the potentiality of this tool, we analyze here a radio burst occurred during an impulsive flare 1B/M6.7 on 10 March 2001 (AR 9368, N27W42). Based on detailed analysis of the spectral, temporal, and spatial relationships, we obtained firm evidence that the microwave continuum burst is produced by electron beams. For the first time we developed and applied a new forward fitting algorithm based on exact gyrosynchrotron formulae and employing both the total power and polarization measurements to solve the inverse problem of the beam diagnostics. We found that the burst is generated by a oblique beam in a region of reasonably strong magnetic field ($\sim 200-300$ G) and the burst is observed at a quasi-transverse viewing angle. We found that the life time of the emitting electrons in the radio source is relatively short, $\tau_l \approx 0.5$ s, consistent with a single reflection of the electrons from a magnetic mirror at the foot point with the stronger magnetic field. We discuss the implications of these findings for the electron acceleration in flares and for beam diagnostics.Comment: Astrophysical Journal, accepted: 26 pages, 8 figure

Evidence of Pentaquark States from K+ N Scattering Data?

Motivated by the recent experimental evidence of the exotic B = S = +1 baryonic state Theta(1540), we examine the older existing data on K+ N elastic scattering through the time delay method. We find positive peaks in time delay around 1.545 and 1.6 GeV in the D03 and P01 partial waves of K+ N scattering respectively, in agreement with experiments. We also find an indication of the J=3/2 Theta* spin-orbit partner to the Theta, in the P03 partial wave at 1.6 GeV. We discuss the pros and contras of these findings in support of the interpretation of these peaks as possible exotics.Comment: 10 pages, 4 figure

A simple model of reactor cores for reactor neutrino flux calculations for the KamLAND experiment

KamLAND is a reactor neutrino oscillation experiment with a very long baseline. This experiment successfully measured oscillation phenomena of reactor antineutrinos coming mainly from 53 reactors in Japan. In order to extract the results, it is necessary to accurately calculate time-dependent antineutrino spectra from all the reactors. A simple model of reactor cores and code implementing it were developed for this purpose. This paper describes the model of the reactor cores used in the KamLAND reactor analysis.Comment: 14 pages, 7 figures, submitted to Nuclear Instruments and Methods in Physics Research