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).
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.
10853977
Lectures on instanton counting
These notes have two parts. The first is a study of Nekrasov's deformed partition functions $Z(\ve_1,\ve_2,\vec{a};\q,\vec{\tau})$ of N=2 SUSY Yang-Mills theories, which are generating functions of the integration in the equivariant cohomology over the moduli spaces of instantons on $\mathbb R^4$. The second is review of geometry of the Seiberg-Witten curves and the geometric engineering of the gauge theory, which are physical backgrounds of Nekrasov's partition functions. 
The first part is continuation of math.AG/0306198, where we identified the Seiberg-Witten prepotential with $Z(0,0,\vec{a};\q,0)$. 
We put higher Casimir operators to the partition function and clarify their relation to the Seiberg-Witten $u$-plane. We also determine the coefficients of $\ve_1\ve_2$ and $(\ve_1^2+\ve_2^2)/3$ (the genus 1 part) of the partition function, which coincide with two measure factors $A$, $B$ appeared in the $u$-plane integral. 
The proof is based on the blowup equation which we derived in the previous paper.
8936511
Instantons and affine Lie algebras
Various constructions of the affine Lie algebra action on the moduli space of instantons on 4-manifolds are discussed. The analogy between the local-global principle and the role of mass is also explained. The detailed proofs are given in separated papers [16,17].
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.
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.
14092663
Roles of the quark field in the infrared lattice Coulomb gauge and Landau gauge QCD
Fac of Infor Sci; Utsunomiya Univ, Utsunomiya, 320-8585 JapanE-mail:nakajima@is.utsunomiya-u.ac.jpThe effective coupling of QCD is measured by using the gauge conﬁgurations produced by theMILC collaboration in which the Kogut Susskind (KS) fermion is incorporated and by using thatproducedby the QCDOC collaborationin which the domain wall fermion (DWF) is incorporated.We ﬁx the gauge to the Landau gauge and to the Coulomb gauge. Th e infrared effective couplingin the Coulomb gauge agrees with the recent extraction at JLab, but that in the Landau gaugeshows infrared suppression. The suppression is expected to be due to the color anti-symmetricghost propagator which in the unquenched conﬁgurations has stronger infrared singularity thanthe color diagonal ghost propagator. The Coulomb form factor in the infrared depends on the kindof the fermion incorporated in the system and the temperature.The quark has the effect of quenching randomness and the ﬂuct uation of the color anti-symmetricghost propagator is reduced in the unquenched conﬁguration , and the Kugo-Ojima parameterc iscloser to 1 in the unquenched conﬁguration than in the quench ed conﬁguration.The XXV International Symposium on Lattice Field TheoryJuly 30 - August 4 2007Regensburg, Germany
18117830
Infrared features of the lattice Landau gauge QCD
The infrared properties of lattice Landau gauge QCD of SU(3) are studied by measuring gluon propagator, ghost propagator, QCD running coupling and Kugo-Ojima parameter of β = 6.0,164, 244, 324 and β = 6.4, 324, 484 lattices. We study Cribov copy problem by parallel tempering (PT) gauge fixing of β = 2.2,164 SU(2) configurations. Rather unexpected features of the unique gauge(fundamental modular gauge, FMC) are observed in relation of physical values vs the optimizing function.
110688155
Development of the analog ASIC for multi-channel readout X-ray CCD camera
Abstract We report on the performance of an analog application-specific integrated circuit (ASIC) developed aiming for the front-end electronics of the X-ray CCD camera system onboard the next X-ray astronomical satellite, ASTRO-H. It has four identical channels that simultaneously process the CCD signals. Distinctive capability of analog-to-digital conversion enables us to construct a CCD camera body that outputs only digital signals. As the result of the front-end electronics test, it works properly with low input noise of ≤ 30 μ V at the pixel rate below 100 kHz. The power consumption is sufficiently low of ∼ 150 mW / chip . The input signal range of ±20 mV covers the effective energy range of the typical X-ray photon counting CCD (up to 20 keV). The integrated non-linearity is 0.2% that is similar as those of the conventional CCDs in orbit. We also performed a radiation tolerance test against the total ionizing dose (TID) effect and the single event effect. The irradiation test using 60 Co and proton beam showed that the ASIC has the sufficient tolerance against TID up to 200 krad, which absolutely exceeds the expected amount of dose during the period of operating in a low-inclination low-earth orbit. The irradiation of Fe ions with the fluence of 5.2×10 8  Ion/cm 2 resulted in no single event latchup (SEL), although there were some possible single event upsets. The threshold against SEL is higher than 1.68 MeV cm 2 /mg, which is sufficiently high enough that the SEL event should not be one of major causes of instrument downtime in orbit.
17493300
Supersymmetric CPN Sigma Model on Noncommutative Superspace
We construct a closed form of the action of the supersymmetric CP N sigma model on noncommutative superspace in four dimensions. We show that this model has N = 1/2 supersymmetry and that the transformation law is not modified. The supersymmetric CP N sigma model on noncommutative superspace in two dimensions is obtained by dimensional reducing the model in four dimensions.
16529601
Theoretical Framework for R-parity Violation
We propose a theoretical framework for R-parity violation. It is realized by a class of Calabi-Yau compactification of heterotic string theory. Trilinear R-parity violation in superpotential is either absent or negligibly small without an unbroken symmetry, due to a selection rule based on charge counting of a spontaneously broken U(1) symmetry. Although such a selection rule cannot be applied in general to nonrenormalizable operators in the low-energy effective superpotential, it is valid for terms trilinear in low-energy degrees of freedom, and hence can be used as a solution to the dimension-4 proton decay problem in the minimal supersymmetric standard model. Bilinear R-parity violation is generated, but there are good reasons why it is small enough to satisfy its upper bounds from neutrino mass and washout of baryon/lepton asymmetry. All R-parity violating dimension-5 operators can be generated. In this theoretical framework, nucleons can decay through squark-exchange diagrams combining dimension-5 and bilinear R-parity violating operators. B ― L breaking neutron decay is predicted.