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.
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.
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.
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.
15379696
Vortex-type Half-BPS Solitons in ABJM Theory
We study Aharony-Bergman-Jafferis-Maldacena (ABJM) theory without and with mass deformation. It is shown that maximally supersymmetry preserving, D-term, and F-term mass deformations of single mass parameter are equivalent. We obtain vortex-type halfBPS equations and the corresponding energy bound. For the undeformed ABJM theory, the resulting half-BPS equation is the same as that in supersymmetric Yang-Mills theory and no finite energy regular BPS solution is found. For the mass-deformed ABJM theory, the halfBPS equations for U(2)×U(2) case reduce to the vortex equation in Maxwell-Higgs theory, which supports static regular multi-vortex solutions. In U(N)×U(N) case with N > 2 the nonabelian vortex equation of Yang-Mills-Higgs theory is obtained.
14784732
Instanton calculus in R-R 3-form background and deformed = 2 super Yang-Mills theory
We study the ADHM construction of instantons in = 2 supersymmetric Yang-Mills theory deformed in constant Ramond-Ramond (R-R) 3-form field strength background in type IIB superstrings. We compare the deformed instanton effective action with the effective action of fractional D3/D(−1) branes at the orbifold singularity of C2/Z2 in the same R-R background. We find discrepancy between them at the second order in deformation parameters, which comes from the coupling of the translational zero modes of the D(−1)-branes to the R-R background. We improve the deformed action by adding a term with space-time dependent gauge coupling. Although the space-time action differs from the action in the Ω-background, both actions lead to the same instanton equations of motion at the lowest order in gauge coupling.
119352385
Unquenched Kogut-Susskind quark propagator in lattice Landau gauge QCD
Quark propagators of the unquenched Kogut-Susskind (KS) fermion obtained from the gauge configurations of the MILC Collaboration are measured after Landau gauge fixing and using the Staple+Naik action. Presence of the qq condensates and A{sup 2} condensates in the dynamical mass M(q) and the quark wave function renormalization Z{sub {psi}}(q{sup 2}) are investigated. We obtain the correlation of the renormalization factor of the running coupling taken at {mu}{approx}6 GeV and that of the quark wave function renormalization Z{sub {psi}}(q{sup 2}) of the Staple+Naik action. The mass function M(q) is finite at q=0 and its chiral limit is {approx}0.38 GeV. We compared the results corrected by the scale of the vertex renormalization and the tadpole renormalization with the corresponding values obtained by the Asqtad action without renormalization and observed good agreement. Implication of infrared finite Z{sub 2}(q)=1/Z{sub {psi}}(q{sup 2}) to the Kugo-Ojima confinement criterion is discussed.
119276786
Proton radiation damage experiment on P-Channel CCD for an X-ray CCD camera onboard the ASTRO-H satellite
Abstract We report on a proton radiation damage experiment on P-channel CCD newly developed for an X-ray CCD camera onboard the ASTRO-H satellite. The device was exposed up to 10 9 protons cm −2 at 6.7 MeV. The charge transfer inefficiency (CTI) was measured as a function of radiation dose. In comparison with the CTI currently measured in the CCD camera onboard the Suzaku satellite for 6 years, we confirmed that the new type of P-channel CCD is radiation tolerant enough for space use. We also confirmed that a charge-injection technique and lowering the operating temperature efficiently work to reduce the CTI for our device. A comparison with other P-channel CCD experiments is also discussed.
119183865
Single event effect characterization of the mixed-signal ASIC developed for CCD camera in space use
Abstract We present the single event effect (SEE) tolerance of a mixed-signal application-specific integrated circuit (ASIC) developed for a charge-coupled device camera onboard a future X-ray astronomical mission. We adopted proton and heavy ion beams at HIMAC/NIRS in Japan. The particles with high linear energy transfer (LET) of 57.9 MeV cm 2 / mg is used to measure the single event latch-up (SEL) tolerance, which results in a sufficiently low cross-section of σ SEL 4.2 × 10 − 11 cm 2 /(Ion×ASIC). The single event upset (SEU) tolerance is estimated with various kinds of species with wide range of energy. Taking into account that a part of the protons creates recoiled heavy ions that have higher LET than that of the incident protons, we derived the probability of SEU event as a function of LET. Then the SEE event rate in a low-earth orbit is estimated considering a simulation result of LET spectrum. SEL rate is below once per 49 years, which satisfies the required latch-up tolerance. The upper limit of the SEU rate is derived to be 1.3×10 −3  events/s. Although the SEU events cannot be distinguished from the signals of X-ray photons from astronomical objects, the derived SEU rate is below 1.3% of expected non-X-ray background rate of the detector and hence these events should not be a major component of the instrumental background.