67838047
A mathematical theory of D-string world-sheet instantons, I: Compactness of the stack of $Z$-semistable Fourier-Mukai transforms from a compact family of nodal curves to a projective Calabi-Yau 3-fold
In a suitable regime of superstring theory, D-branes in a Calabi-Yau space and their most fundamental behaviors can be nicely described mathematically through morphisms from Azumaya spaces with a fundamental module to that Calabi-Yau space. In the earlier work [L-L-S-Y] (D(2): arXiv:0809.2121 [math.AG], with Si Li and Ruifang Song) from the project, we explored this notion for the case of D1-branes (i.e. D-strings) and laid down some basic ingredients toward understanding the notion of D-string world-sheet instantons in this context. In this continuation, D(10), of D(2), we move on to construct a moduli stack of semistable morphisms from Azumaya nodal curves with a fundamental module to a projective Calabi-Yau 3-fold $Y$. In this Part I of the note, D(10.1), we define the notion of twisted central charge $Z$ for Fourier-Mukai transforms of dimension 1 and width [0] from nodal curves and the associated stability condition on such transforms and prove that for a given compact stack of nodal curves $C_{\cal M}/{\cal M}$, the stack $FM^{1,[0];Zss}_{C_{\cal M}/{\cal M}}(Y,c)$ of $Z$-semistable Fourier-Mukai transforms of dimension 1 and width [0] from nodal curves in the family $C_{\cal M}/{\cal M}$ to $Y$ of fixed twisted central charge $c$ is compact. For the application in the sequel D(10.2), $C_{\cal M}/{\cal M}$ will contain $C_{\bar{\cal M}_g}/\bar{\cal M}_g$ as a substack and $FM^{1,[0];Zss}_{C_{\cal M}/{\cal M}}(Y,c)$ in this case will play a key role in defining stability condition for morphisms from arbitrary Azumaya nodal curves (with the underlying nodal curves not necessary in the family $C_{\cal M}/{\cal M}$) to $Y$.
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.
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
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.
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.
118527003
Strong gravitational lensing of quasi-Kerr compact object with arbitrary quadrupole moments
A bstractWe study the strong gravitational lensing on the equatorial plane of a quasi-Kerr compact object with arbitrary quadrupole moments which can be used to model the super-massive central object of the galaxy. We find that, when the quadrupolar correction parameter ξ takes the positive (negative) value, the photon-sphere radius rps, the minimum impact parameter ups, the coefficient $ \overline b $, the relative magnitudes rm and the angular position of the relativistic images θ∞ are larger (smaller) than the results obtained in the Kerr black hole, but the coefficient $ \overline a $, the deflection angle α(θ) and the angular separation s are smaller (larger) than that in the Kerr black hole. These features may offer a way to probe special properties for some rotating compact objects by the astronomical instruments in the future.
34826696
Lattice study of radiative J/ψ decay to a tensor glueball.
The radiative decay of J/ψ into a pure gauge tensor glueball is studied in the quenched lattice QCD formalism. With two anisotropic lattices, the multipole amplitudes E1(0), M2(0), and E3(0) are obtained to be 0.114(12)(6) GeV, -0.011(5)(1)  GeV, and 0.023(8)(1) GeV, respectively. The first error comes from the statistics, the Q2 interpolation, and the continuum extrapolation, while the second is due to the uncertainty of the scale parameter r0(-1)=410(20)  MeV. Thus, the partial decay width Γ(J/ψ→γG(2++)) is estimated to be 1.01(22)(10) keV, which corresponds to a large branch ratio 1.1(2)(1)×10(-2). The phenomenological implication of this result is also discussed.
118638173
Strong gravitational lensing in a black-hole spacetime dominated by dark energy
We study the influence of phantom fields on strong field gravitational lensing. Supposing that the gravitational field of the supermassive central object of the Galaxy is described by a phantom black hole metric, we estimate the numerical values of the coefficients and observations and find that the influence of the phantom fields is somewhat similar to that of the electric charge in a Reissner-Nordstrom black hole, i.e., the deflect angle and angular separation increase with the phantom constant b. However, other observations are contrary to the Reissner-Nordstrom case and show the effects of dark energy, such as (i) compressing the usual black hole and more powerfully attracting photons, (ii) making the relativistic Einstein ring larger than that of the usual black hole, and (iii) not weakening the usual relative magnitudes, which will facilitate observations.
117744661
Glueballs in charmonia radiative decays
Scalar [1] and tensor [2] glueballs created in J/ψ radiative decays are studied in quenched lattice QCD. Using two anisotropic lattices to approach the continuum limit, we compute the relevant form factors responsible for the decay rates for J/ψ → γG0++ and J/ψ → γG2++ . Comparing with the existing experimental data, it is argued that f0(1710) is a favorable candidate for scalar glueball. The decay rate for J/ψ → γG2++ is found to be quite substantial. A comprehensive search in the tensor channel on BESIII is therefore suggested.
1136207
Four light neutrinos in the singular seesaw mechanism with Abelian flavor symmetry
The four light neutrino scenario, which explains the atmosphere, solar and LSND neutrino experiments, is studied in the framework of the seesaw mechanism. By taking both the Dirac and Majorana mass matrix of neutrinos to be singular, the four neutrino mass spectrum consisting of two almost degenerate pairs separated by a mass gap $\sim 1$ eV is naturally generated. Moreover the right-handed neutrino Majorana mass can be at $\sim 10^{14}$ GeV scale unlike in the usual singular seesaw mechanism. Abelian flavor symmetry is used to produce the required neutrino mass pattern. A specific example of the flavor charge assignment is provided to show that maximal mixings between the $\nu_\mu-\nu_\tau$ and $\nu_e-\nu_s$ are respectively attributed to the atmosphere and solar neutrino anomalies while small mixing between two pairs to the LSND results. The implication in the other fermion masses is also discussed.