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.
119132882
Refined Chern-Simons theory and Hilbert schemes of points on the plane
Dedicated to Professor Igor Frenkel on the occasion of his sixtieth birthday Abstract. Aganagic and Shakirov propose a refinement of the SU(N) Chern- Simons theory for links in three manifolds with S 1 -symmetry, such as torus knots in S 3 , based on deformation of the S and T matrices, originally found by Kirillov and Cherednik. We relate the large N limit of the S matrix to the Hilbert schemes of points on the affine plane. As an application, we find an explicit formula for the Euler characteristics of the universal sheaf, applied arbitrary Schur functor.
14508627
PERVERSE COHERENT SHEAVES ON BLOW-UP. II. WALL-CROSSING AND BETTI NUMBERS FORMULA
This is the second of series of papers studyig moduli spaces of a certain class of coherent sheaves, which we call stable perverse coherent sheaves, on the blow-up p: b X → X of a projective surface X at a point 0. The followings are main results of this paper: a) We describe the wall-crossing between moduli spaces caused by twisting of the line bundle O(C) associated with the exceptional divisor C. b) We give the formula for virtual Hodge numbers of moduli spaces of stable perverse coherent sheaves. Moreover we also give proofs of the followings which we observed in a special case in (24): c) The moduli space of stable perverse coherent sheaves is isomorphic to the usual moduli space of stable coherent sheaves on the original surface if the first Chern class is orthogonal to (C). d) The moduli space becomes isomorphic to the usual moduli space of stable coherent sheaves on the blow-up after twisting by O(−mC) for sufficiently largem. Therefore usual moduli spaces of stable sheaves on the blow-up and the original surfaces are connected via wall-crossings.
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).
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.
56216283
K-theoretic Donaldson invariants via instanton counting
In this paper we study the holomorphic Euler characteristics of determinant line bundles on moduli spaces of rank 2 semistable sheaves on an algebraic surface X, which can be viewed as $K$-theoretic versions of the Donaldson invariants. In particular, if X is a smooth projective toric surface, we determine these invariants and their wallcrossing in terms of the K-theoretic version of the Nekrasov partition function (called 5-dimensional supersymmetric Yang-Mills theory compactified on a circle in the physics literature). Using the results of math.AG/0606180 we give an explicit generating function for the wallcrossing of these invariants in terms of elliptic functions and modular forms.
118929109
A Systematic Study of X-Ray Flares from Low-Mass Young Stellar Objects in the $\rho$ Ophiuchi Star-Forming Region with Chandra
We report on the results of a systematic study of X-ray flares from low-mass young stellar objects, using two deep exposure Chandra observations of the main region of the ρ Ophiuchi star-forming cloud. From 195 X-ray sources, including class I-III sources and some young brown dwarfs, we detected a total of 71 X-ray flares. Most of the flares have the typical profile of solar and stellar flares, fast rise and slow decay, while some bright flares show unusually long rise timescales. We derived the time-averaged temperature (� kT � ), luminosity (� LX� ), rise and decay timescales (τr and τd) of the flares, finding that (1) class I-II sources tend to have a highkT � , which sometimes exceeds 5keV, (2) the distribution ofLXduring flares is nearly the same for all classes from ∼10 29.5 to ∼10 31.5 ergs −1 , although there is a marginal hint of a higherLXdistribution for class I than class II-III, and (3) positive and negative log-linear correlations are found between τr and τd ,a ndkTand τr. In order to explain these relations, we used the framework of magnetic reconnection model with heat conduction and chromospheric evaporation to formulate the observational parameters (τr, τd ,a ndkT� ) as a function of the pre-flare (coronal) electronic density (nc), the half-length of the reconnected magnetic loop (L), and magnetic field strength (B). The observed correlations are well reproduced if loop lengths are nearly the same for all classes, regardless of the existence of an accretion disk. The estimated loop length is almost comparable to the typical stellar radius of these objects (10 10 -10 11 cm), which indicates that the observed flares are triggered by solar-type loops, rather than larger ones (∼ 10 12 cm) connecting the star with its inner accretion disk. The higherkTobserved for class I sources may be explained by a slightly higher magnetic field strength (≈ 500G) than for class II-III sources (200-300G).
2668770
Coupling between M2-branes and form fields
In the context of low-energy effective theory of multiple M2-branes, we construct the interaction terms between the world-volume fields of M2-branes and the antisymmetric tensor fields of three- and six-forms. By utilizing the compactification procedure, we show coincidence between the dimensionally reduced coupling and the R-R coupling to D-branes in type II string theory. We also discuss that a cubic term proportional to six-form field reproduces the quartic mass-deformation term in the world-volume theory of multiple M2-branes.
119514655
What the Gribov copy tells about confinement and the theory of dynamical chiral symmetry breaking
We performed lattice Landau gauge QCD simulation on {beta}=6.0,16{sup 4},24{sup 4},32{sup 4} and {beta}=6.4,32{sup 4},48{sup 4} and 56{sup 4} by adopting the gauge fixing that minimizes the norm of the gauge field, and measured the running coupling by using the gluon propagator and the ghost propagator. In view of ambiguity in the vertex renormalization factor Z{sub 1} in the lattice, we adjust the normalization of the running coupling by the perturbative QCD results near the highest momentum point. It has a maximum {alpha}{sub s}(q){approx_equal}2.1(3) at around q=0.5 GeV and decreases as q approaches 0, and the Kugo-Ojima parameter reached -0.83(2). The infrared exponent of the ghost propagator at 0.4 GeV region is {alpha}{sub G}=0.20 but there is an exceptional Gribov copy with {alpha}{sub G}=0.27. The features of the exceptional Gribov copy are investigated by measuring four one-dimensional Fourier transform (1-d FT) of the gluon propagator transverse to each lattice axis. We observe, in general, correlation between absolute value of the Kugo-Ojima parameter and the degree of reflection positivity violation in the 1-d FT of the gluon propagator. The 1-d FT of the exceptional Gribov copy has an axis whose samplewise gluon propagator manifestly violates reflection positivity, and the average ofmore » the Cartan subalgebra components of the Kugo-Ojima parameter along this axis is consistent to -1. The running coupling of the ensemble average shows a suppression at 0 momentum, but when the ghost propagator of the exceptional Gribov copy is adopted, the suppression disappears and the data implies presence of the infrared fixed point {alpha}{sub s}(0){approx}2.5(5) and {kappa}=0.5 suggested by the Dyson-Schwinger approach in the multiplicative renormalizable scheme. Comparison with the SU(2) QCD and N{sub f}=2 unquenched SU(3) QCD are also made.« less
17703115
X-Ray Observation on the Monoceros R2 Star-Forming Region with the Chandra ACIS-I Array
We report on the results of the Chandra ACIS-I observation on the central region of the Monoceros R2 cloud (Mon R2), a high-mass star-forming region (SFR) at a distance of 830pc. With a deep exposure of ∼ 100ks, we detected 368 X-ray sources, ∼80% of which were identified with the near-infrared (NIR) counterparts. We systematically analyzed the spectra and time variability of most of the X-ray emitting sources and provided a comprehensive X-ray source catalog for the first time. Using the J-, H-, and K-band magnitudes of the NIR counterparts, we estimated the evolutionary phase (classical T Tauri stars and weak-lined T Tauri stars) and the mass of the X-ray emitting sources, and analyzed the X-ray properties as a function of the age and mass. We found a marginal hint that classical T Tauri stars have a slightly higher temperature (2.4keV) than that of weak-lined T Tauri stars (2.0keV). A significant fraction of the high- and intermediate-mass sources have a time variability and high plasma temperatures (2.7keV) similar to those of low-mass sources (2.0keV). We performed the same analysis for other SFRs, the Orion Nebula Cluster and Orion Molecular Cloud-2/3, and obtained similar results to Mon R2. This supports the earlier results of this observation obtained by Kohno et al. (2002, ApJ, 567, 423) and Preibisch et al. (2002, A&A, 392, 945) that high- and intermediate-mass young stellar objects emit X-rays via magnetic activity. We also found a significant difference in the spatial distribution between X-ray and NIR sources.
17235598
A New Supernova Remnant Candidate and an Associated Outflow in the Sagittarius C Region
We present the Suzaku results on a new candidate of a supernova remnant (SNR) in the Sagittarius C region. We detected diffuse X-rays of an elliptical shape (G359.41-0.12) and a chimney-like structure (the Chimney), both of which were fitted with a thin thermal the model of kBT ~1 keV temperature. The absorption columns are same between these two structures, indicating that both are located at the same distance in the same line of sight. The narrow band image and one-dimensional profile of S XV Kalpha at 2.45 keV show that the Chimney is emanating from G359.41-0.12. Therefore, these two sources are physically connected with each other. The sum of the thermal energies of the Chimney and G359.41-0.12 is estimated to be 1.4x10^50 erg, typical for a galactic SNR. G359.41-0.12 is likely to be a new SNR candidate and the Chimney is an associated outflow.