873508
t-analogs of q-characters of Kirillov-Reshetikhin modules of quantm affine algebras
We prove the Kirillov-Reshetikhin conjecture concerning certain finite dimensional representations of a quantum affine algebra $\Ua$ when $\hat\g$ is an untwisted affine Lie algebra of type $ADE$. We use $t$--analog of $q$--characters introduced by the author in an essential way.
73636075
Quiver Varieties and Tensor Products, II
We define a family of homomorphisms on a collection of convolution algebras associated with quiver varieties, which gives a kind of coproduct on the Yangian associated with a symmetric Kac-Moody Lie algebra. We study its property using perverse sheaves.
119569923
Instanton counting on blowup. II. K-theoretic partition
function
AbstractWe study Nekrasov's deformed partition function $Z(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta)$ of 5-dimensional supersymmetric
Yang-Mills theory compactified on a circle. Mathematically it is the
generating function of the characters of the coordinate rings of the moduli
spaces of instantons on $\mathbb R^4$. We show that it satisfies a system of
functional equations, called blowup equations, whose solution is unique.
As applications, we prove (a) $F(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta) = \varepsilon_1\varepsilon_2 \log Z(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta)$ is regular at $\varepsilon_1 = \varepsilon_2 = 0$ (a part of Nekrasov's conjecture), and (b) the genus $1$ parts, which are first several Taylor coefficients of $F(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta)$, are written explicitly in terms of $\tau = d^2 F(0,0,\vec{a};\mathfrak q,\boldsymbol\beta)/da^2$ in rank $2$ case.
14815866
Handsaw quiver varieties and finite W-algebras
Following Braverman-Finkelberg-Feigin-Rybnikov (arXiv:1008.3655), we study the convolution algebra of a handsaw quiver variety, a.k.a. a parabolic Laumon space, and a finite W-algebra of type A. This is a finite analog of the AGT conjecture on 4-dimensional supersymmetric Yang-Mills theory with surface operators. Our new observation is that the C^*-fixed point set of a handsaw quiver variety is isomorphic to a graded quiver variety of type A, which was introduced by the author in connection with the representation theory of a quantum affine algebra. As an application, simple modules of the W-algebra are described in terms of IC sheaves of graded quiver varieties of type A, which were known to be related to Kazhdan-Lusztig polynomials. This gives a new proof of a conjecture by Brundan-Kleshchev on composition multiplicities on Verma modules, which was proved by Losev, in a wider context, by a different method.
16014956
Instanton counting and Donaldson invariants
For a smooth projective toric surface we determine the Donaldson invariants and their wallcrossing in terms of the Nekrasov partition function. Using the solution of the Nekrasov conjecture (33, 38, 3) and its refinement (34), we apply this result to give a generating function for the wallcrossing of Donaldson invariants of good walls of simply connected projective surfaces with b+ = 1 in terms of modular forms. This formula was proved earlier in (19) more generally for simply connected 4-manifolds with b+ = 1, assuming the Kotschick-Morgan conjecture and it was also derived by physical arguments in (31).
15725379
Counting invariant of perverse coherent sheaves and its wall-crossing
We introduce moduli spaces of stable perverse coherent systems on small crepant resolutions of Calabi-Yau 3-folds and consider their Donaldson-Thomas type counting invariants. The stability depends on the choice of a component (= a chamber) in the complement of finitely many lines (= walls) in the plane. We determine all walls and compute generating functions of invariants for all choices of chambers when the Calabi-Yau is the resolved conifold. For suitable choices of chambers, our invariants are specialized to Donaldson-Thomas, Pandharipande-Thomas and Szendroi invariants.
118853198
Quantum SUSY algebra of Q-lumps in the massive Grassmannian sigma model
We compute the SUSY algebra of the massive Grassmannian sigma model in (2+1) dimensions. We first rederive the action of the model by using Scherk–Schwarz dimensional reduction from theory in (3+1) dimensions. Then, we perform canonical quantization by using the Dirac method. We find that a particular choice of the operator ordering yields the quantum SUSY algebra of Q-lumps with central extension.
118654045
Imaging Spectroscopy on Preflare Coronal Nonthermal Sources Associated with the 2002 July 23 Flare
We present a detailed examination on the coronal nonthermal emissions during the preflare phase of the X4.8 flare that occurred on 2002 July 23. The microwave (17 GHz and 34 GHz) data obtained with Nobeyama Radioheliograph, at Nobeyama Solar Radio Observatory and the hard X-ray (HXR) data taken with RHESSI obviously showed nonthermal sources that are located above the flare loops during the preflare phase. We performed imaging spectroscopic analyses on the nonthermal emission sources both in microwaves and in HXRs, and confirmed that electrons are accelerated from several tens of keV to more than 1 MeV even in this phase. If we assume the thin-target model for the HXR emission source, the derived electron spectral indices (~4.7) is the same value as that from microwaves (~4.7) within the observational uncertainties, which implies that the distribution of the accelerated electrons follows a single power law. The number density of the microwave-emitting electrons is, however, larger than that of the HXR-emitting electrons, unless we assume low-ambient plasma density of about 1.0 × 109 cm–3 for the HXR-emitting region. If we adopt the thick-target model for the HXR emission source, on the other hand, the electron spectral index (~6.7) is much different, while the gap of the number density of the accelerated electrons is somewhat reduced.
115937003
Construction of a two-magnet type broad range particle analyzer and measurement of ion-optical properties by use of it.
53532682
Effects of the quark field on the ghost propagator of lattice Landau gauge QCD
Infrared features of the ghost propagator of color-diagonal and color antisymmetric ghost propagator of quenched SU(2) and quenched SU(3) are compared with those of unquenched Kogut-Susskind fermion SU(3) lattice Landau gauge. We compare (i) the fluctuation of the ghost propagator (ii) the ghost condensate parameter v of the local composite operator (LCO) approach, and (iii) the Binder cumulant of color antisymmetric ghost propagator between quenched and unquenched configurations. The color-diagonal SU(3) ghost dressing function of unquenched configurations has weaker singularity than the quenched configurations. In both cases fluctuations become large in q /( ){sup 2}), where {phi}-vector(q) is the color antisymmetric ghost propagator measured by the sample average of gauge fixed configurations via parallel tempering method, becomes {approx}4/9 in all the momentum region. The Binder cumulant of the color antisymmetric ghost propagator of quenched SU(2) can be explained by the 3D Gaussian distribution, but that of the unquenched MILC{sub c} deviates slightly from that of the eight-dimensional Gaussian distribution. The strongermore » singularity and large fluctuation in the quenched configuration could be the cause of the deviation of the Kugo-Ojima confinement parameter c from 1, and the presence of ordering in the ghost propagator of unquenched configurations makes it closer to 1.« less
11444415
A detailed observation of a LMC supernova remnant DEM L241 with XMM-Newton
We report on an XMM-Newton observation of the supernova remnant (SNR) DEM L241 in the Large Magellanic Cloud. In the soft band image, the emission shows an elongated structure, like a killifish, with a central compact source. The compact source is point-like, and named XMMU J053559.3-673509. The source spectrum is reproduced well by a power-law model with a photon index of $\Gamma = 1.57$ (1.51–1.62); and the intrinsic luminosity is 2.2 $\times$ $10^{35}~{\rm erg~s^{-1}}$ in the 0.5–10.0 keV band, with an assumed distance of 50 kpc. The source has neither significant coherent pulsations in 2.0 $\times$ 10 -3 –8.0 Hz nor time variabilities. Its luminosity and spectrum suggest that the source might be a pulsar wind nebula (PWN) in DEM L241. The spectral feature classifies this source as rather bright and hard PWN, which is similar to those in Kes 75 and B0540-693. The elongated diffuse structure can be divided into a “Head” and “Tail”, and both have soft and line-rich spectra. Their spectra are reproduced well by a plane-parallel shock plasma ( vpshock ) model with a temperature of 0.3–0.4 keV, over-abundance in O and Ne, and a relative under-abundance in Fe. Such an abundance pattern and the morphology imply both that the emission is from the ejecta of the SNR and that the progenitor of DEM L241 is a very massive star, more than 20 $M_\odot$. This result is also supported by the existence of the central point source and an OB star association, LH 88. The total thermal energy and plasma mass are ~4 $\times$ 10 50 erg and ~$200~M_\odot$, respectively.