115174219
D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck
In this continuation of (L-Y3) (arXiv:0709.1515 (math.AG)), (L-L-S-Y) (arXiv:0809.2121 (math.AG)), (L-Y4) (arXiv:0901.0342 (math.AG)), (L-Y5) (arXiv:0907.0268 (math.AG)), and (L-Y6) (arXiv:0909.2291 (math.AG)), we give an overview of the posted part of the project and then take it as background to introduce Azumaya noncommutative C ∞ -manifold and the four aspects of morphisms therefrom to a projective complex manifold. This gives us then a description of supersymmetric D-branes of A-type in a Calabi-Yau manifold along the line of the Polchinski-Grothendieck Ansatz. The notion of Kahler differentials and their tensors for an Azumaya noncommutative space are introduced. Donaldson's picture of Lagrangian and special Lagrangian submanifolds as selected from the zero-locus of a moment-map on a related space of maps can be merged into the setting of morphisms from Azumaya man- ifolds with a fundamental module. As a pedagogical toy model for illustration, we study D-branes of A-type in a Calabi-Yau torus. Simple as it is, it reveals already several features of D-branes of A-type, including their assembling/disassembling. The short-vs.-long string wrapping behavior of matrix-strings in the string-theory literature can be produced in this context as well. In addition to the previous comparison with stringy works made, the 4th theme (subtitled: "Gomez-Sharpe vs. Polchinski-Grothendieck") of Sec. 2.4 is to be read with the work (G-Sh) (arXiv:hep-th/0008150), while the 2nd theme (subtitled: "Donagi- Katz-Sharpe vs. Polchinski-Grothendieck") of Sec. 4.2 is to be read with the work (D-K-S) (arXiv:hep-th/0309270). Sec. 4.3, though not yet ready to be subtitled "Denef vs. Polchinski- Grothendieck", is to be read with the work (De) (arXiv:hep-th/0107152). Some directly related string-theory remarks are added to the end of each section.
40162216
Azumaya noncommutative geometry and D-branes: An Origin of the master nature of D-branes
In this lecture I review how a matrix/Azumaya-type noncommutative geometry arises for D-branes in string theory and how such a geometry serves as an origin of the master nature of D-branes; and then highlight an abundance conjecture on D0-brane resolutions of singularities that is extracted and purified from a work of Douglas and Moore in 1996. A conjectural relation of our setting with `D-geometry' in the sense of Douglas is also given. The lecture is based on a series of works on D-branes with Shing-Tung Yau, and in part with Si Li and Ruifang Song.
18184003
On the splitting type of an equivariant vector bundle over a toric manifold
From the work of Lian, Liu, and Yau on ”Mirror Principle”, in the explicit computation of the Euler data Q = { Q0, Q1, � � � } for an equivariant concavex bundle E over a toric manifold, there are two places the structure of the bundle comes into play: (1) the multiplicative characteric class Q0 of V one starts with, and (2) the splitting type of E. Equivariant bundles over a toric manifold has been classified by Kaneyama, using data related to the linearization of the toric action on the base toric manifold. In this article, we relate the splitting type of E to the classifying data of Kaneyama. From these relations, we compute the splitting type of a couple of nonsplittable equivariant vector bundles over toric manifolds that may be of interest to string theory and mirror symmetry. A code in Mathematica that carries out the computation of some of these examples is attached.
341730
Target-space duality between simple compact Lie groups and Lie algebras under the Hamiltonian formalism: I. Remnants of duality at the classical level
AbstractIt has been suggested that a possible classical remnant of the phenomenon of target-space duality (T-duality) would be the equivalence of the classical string Hamiltonian systems. Given a simple compact Lie groupG with a bi-invariant metric and a generating function Γ suggested in the physics literature, we follow the above line of thought and work out the canonical transformation Φ generated by Γ together with an Ad-invariant metric and a B-field on the associated Lie algebra
$$\mathfrak{g}$$
 ofG so thatG and
$$\mathfrak{g}$$
 form a string target-space dual pair at the classical level under the Hamiltonian formalism. In this article, some general features of this Hamiltonian setting are discussed. We study properties of the canonical transformation Φ including a careful analysis of its domain and image. The geometry of the T-dual structure on
$$\mathfrak{g}$$
 is lightly touched. We leave the task of tracing back the Hamiltonian formalism at the quantum level to the sequel of this paper.
116949875
A Degeneration formula of Gromov-Witten invariants with respect to a curve class for degenerations from blow-ups
In two very detailed, technical, and fundamental works, Jun Li constructed a theory of Gromov-Witten invariants for a singular scheme of the gluing form Y1 ∪D Y2 that arises from a degeneration W/A 1 and a theory of relative Gromov-Witten invariants for a codimension-1 relative pair (Y,D). As a summit, he derived a degeneration formula that relates a finite summation of the usual Gromov-Witten invariants of a general smooth fiber Wt of W/A 1 to the Gromov-Witten invariants of the singular fiber W0 = Y1 ∪D Y2 via gluing the relative pairs (Y1,D) and (Y2,D). The finite sum mentioned above depends on a relative ample line bundle H on W/A 1 . His theory has already applications to string theory and mathematics alike. For other new applications of Jun Li’s theory, one needs a refined degeneration formula that depends
14577943
Lorentz Surfaces and Lorentzian CFT --- with an appendix on quantization of string phase space
The interest in string Hamiltonian system has recently been rekindled due to its application to target-space duality. In this article, we explore another direction it motivates. In Sec.\ 1, conformal symmetry and some algebraic structures of the system that are related to interacting strings are discussed. These lead one naturally to the study of Lorentz surfaces in Sec.\ 2. In contrast to the case of Riemann surfaces, we show in Sec.\ 3 that there are Lorentz surfaces that cannot be conformally deformed into Mandelstam diagrams. Lastly in Sec.\ 4, we discuss speculatively the prospect of Lorentzian conformal field theory. 
Additionally, to have a view of what quantum picture a string Hamiltonian system may lead to, we discuss independently in the Appendix a formal geometric quantization of the string phase space.
119253117
SPACETIME NONCOMMUTATIVE EFFECT ON BLACK HOLE AS PARTICLE ACCELERATORS
We study the spacetime noncommutative effect on black hole as particle accelerators and, find that the particles falling from infinity with zero velocity cannot collide with unbound energy, either near the horizon or on the prograde ISCO when the noncommutative Kerr black hole is exactly extremal. Our results also show that the bigger of the spinning black hole's mass is the higher of center of mass energy that the particles obtain. For small and medium noncommutative Schwarzschild black hole, the collision energy depends on the black hole's mass.
43722033
Topological susceptibility near T-c in SU(3) gauge theory
Abstract Topological charge susceptibility χ t for pure gauge SU(3) theory at finite temperature is studied using anisotropic lattices. The over-improved stout-link smoothing method is utilized to calculate the topological charge. Near the phase transition point we find a rapid declining behavior for χ t with values decreasing from ( 188 ( 1 )  MeV ) 4 to ( 67 ( 3 )  MeV ) 4 as the temperature increased from zero temperature to 1.9 T c which demonstrates the existence of topological excitations far above T c . The 4th order cumulant c 4 of topological charge, as well as the ratio c 4 / χ t is also investigated. Results of c 4 show step-like behavior near T c while the ratio at high temperature agrees with the value as predicted by the diluted instanton gas model.
11586065
Scenario of light sterile neutrinos with a heavy tau neutrino in a supersymmetric model
Three light sterile neutrinos (nu (s)(e), nu (s)(mu) and nu (s)(tau)) are introduced to accommodate all the available neutrino data: the atmospheric neutrino anomaly is explained by nu (mu)-nu (s)(mu) oscillation with maximal mixing; the solar one is due to nu (e)-nu (s)(e) oscillation of small angle Mikheyev-Smirnov-Wolfenstein type; the Liquid Scintillation Neutrino Detector data is from v(e)-v(mu) oscillations, so that the neutrinos can be the hot component of the dark matter. The big bang nucleosynthesis constraint is satisfied by taking the tau neutrino to be 10 MeV heavy. The nu (tau) decay is discussed in a model of gauge mediated supersymmetry breaking. The decay mode v(tau) --> (G) over tilde gamma with (G) over tilde being the gravitino is proposed. The nu (tau) has a rather long lifetime similar to 10(3)-10(13) s. Its implication to the gamma-ray burst is discussed. (C) 2001 Elsevier Science B.V. All rights reserved.
53350387
Ultracold-neutron production in a pulsed-neutron beam line
We present the results of an Ultracold neutron (UCN) production experiment in a pulsed neutron beam line at the Los Alamos Neutron Scattering Center. The experimental apparatus allows for a comprehensive set of measurements of UCN production as a function of target temperature, incident neutron energy, target volume, and applied magnetic field. However, the low counting statistics of the UCN signal expected can be overwhelmed by the large background associated with the scattering of the primary cold neutron flux that is required for UCN production. We have developed a background subtraction technique that takes advantage of the very different time-of-flight profiles between the UCN and the cold neutrons, in the pulsed beam. Using the unique timing structure, we can reliably extract the UCN signal. Solid ortho-D2 is used to calibrate UCN transmission through the apparatus, which is designed primarily for studies of UCN production in solid O2. In addition to setting the overall detection efficiency in the apparatus,UCN production data using solid D2 suggest that the UCN upscattering cross-section is smaller than previous estimates, indicating the deficiency of the incoherent approximation widely used to estimate inelastic cross-sections in the thermal and cold regimes.
119184357
Productions of heavy charged leptons via gluon fusion at the LHC: A revisit
Heavy charged lepton productions via gluon fusion at the LHC are revisited. Full loop calculations are adopted with an updated parton distribution function and electroweak data. Including contribution from new generation quarks in the loop, pair production of the sequential heavy lepton via gluon fusion at the LHC dominates over that via the Drell-Yan mechanism in some heavy lepton mass range. Exotic lepton single production of vectorlike lepton extended models is also calculated. In the later case, the gluon fusion mechanism via the Higgs exchange is emphasized. Our numerical results for both pair and single production of heavy leptons are smaller than previous studies especially for a large heavy lepton mass as a result of full loop calculation and due to the mixing angles.