15607702
Extracting Gromov-Witten invariants of a conifold from semi-stable reduction and relative GW invariants of pairs
The study of open/closed string duality and large N duality suggests a GromovWitten theory for conifolds that sits on the border of both a closed Gromov-Witten theory and an open Gromov-Witten theory. The work of Jun Li on Gromov-Witten theory for a projective singular variety of the gluing form Y1 ∪D Y2, where D is a smooth divisor on smooth Y1 and Y2, suggests two methods to study Gromov-Witten invariants for a projective conifold: one by a direct generalization of his construction to the conifold singularity and the other by an appropriate semi-stable reduction of a degeneration to a conifold and then apply his results on this new degeneration to extract Gromov-Witten invariants of the original conifold. In this work we carry out the second method. Suggested by the semi-stable reduction, we associate to a conifold
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
119743554
A mathematical theory of D-string world-sheet instantons, II: Moduli stack of $Z$-(semi)stable morphisms from Azumaya nodal curves with a fundamental module to a projective Calabi-Yau 3-fold
In this Part II, D(10.2), of D(10), we take D(10.1) (arXiv:1302.2054 [math.AG]) as the foundation to define the notion of $Z$-semistable morphisms from general Azumaya nodal curves, of genus $\ge 2$, with a fundamental module to a projective Calabi-Yau 3-fold and show that the moduli stack of such $Z$-semistable morphisms of a fixed type is compact. This gives us a counter moduli stack to D-strings as the moduli stack of stable maps in Gromov-Witten theory to the fundamental string. It serves and prepares for us the basis toward a new invariant of Calabi-Yau 3-fold that captures soft-D-string world-sheet instanton numbers in superstring theory. This note is written hand-in-hand with D(10.1) and is to be read side-by-side with ibidem.
14489670
Nontrivial Azumaya noncommutative schemes, morphisms therefrom, and their extension by the sheaf of algebras of differential operators: D-branes in a B-field background a la Polchinski-Grothendieck Ansatz
In this continuation of [L-Y1], [L-L-S-Y], [L-Y2], and [L-Y3] (arXiv:0709.1515 [math.AG], arXiv:0809.2121 [math.AG], arXiv:0901.0342 [math.AG], arXiv:0907.0268 [math.AG]), we study D-branes in a target-space with a fixed $B$-field background $(Y,\alpha_B)$ along the line of the Polchinski-Grothendieck Ansatz, explained in [L-Y1] and further extended in the current work. We focus first on the gauge-field-twist effect of $B$-field to the Chan-Paton module on D-branes. Basic properties of the moduli space of D-branes, as morphisms from Azumaya schemes with a twisted fundamental module to $(Y,\alpha_B)$, are given. For holomorphic D-strings, we prove a valuation-criterion property of this moduli space. The setting is then extended to take into account also the deformation-quantization-type noncommutative geometry effect of $B$-field to both the D-brane world-volume and the superstring target-space(-time) $Y$. This brings the notion of twisted ${\cal D}$-modules that are realizable as twisted locally-free coherent modules with a flat connection into the study. We use this to realize the notion of both the classical and the quantum spectral covers as morphisms from Azumaya schemes with a fundamental module (with a flat connection in the latter case) in a very special situation. The 3rd theme (subtitled "Sharp vs. Polchinski-Grothendieck") of Sec. 2.2 is to be read with the work [Sh3] (arXiv:hep-th/0102197) of Sharp while Sec. 5.2 (subtitled less appropriately "Dijkgraaf-Holland-Su{\l}kowski-Vafa vs. Polchinski-Grothendieck") is to be read with the related sections in [D-H-S-V] (arXiv:0709.4446 [hep-th]) and [D-H-S] (arXiv:0810.4157 [hep-th]) of Dijkgraaf, Hollands, Su{\l}kowski, and Vafa.
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.
118586717
Generalized Lüscher formula in multichannel baryon-meson scattering
L\"uscher's formula relates the elastic scattering phase shifts to the two-particle energy levels in a finite cubic box. The original formula was obtained for elastic scattering of two massive spinless particles in the center of mass frame. In this paper, we consider the case for the scattering of a spin 1/2 particle with a spinless particle in multi-channel scattering. A generalized relation between the energy of two particle system and the scattering matrix elements is established. We first obtain this relation using quantum-mechanics in both center-of-mass frame and in a general moving frame. The result is then generalized to quantum field theory using methods outlined in Ref. \cite{Hansen:2012tf}. We verify that the results obtained using both methods are equivalent up to terms that are exponentially suppressed in the box size.
119236514
Scalar Glueball in Radiative J/psi Decay on the Lattice
The form factors in the radiative decay of J/psi to a scalar glueball are studied within quenched lattice QCD on anisotropic lattices. The continuum extrapolation is carried out by using two different lattice spacings. With the results of these form factors, the partial width of J/psi radiatively decaying into the pure gauge scalar glueball is predicted to be 0.35(8) keV, which corresponds to a branching ratio of 3.8(9) x 10(-3). By comparing with experiments, out results indicate that f(0)(1710) has a larger overlap with the pure gauge glueball than other related scalar mesons. DOI: 10.1103/PhysRevLett.110.021601
117463737
A Supersymmetric model with the gauge symmetry SU(3)(1) x SU(2)(1) x U(1)(1) x SU(3)(2) x SU(2)(2) x U(1)(2)
A supersymmetric model with two copies of the Standard Model gauge groups is constructed in the gauge mediated supersymmetry breaking scenario. The supersymmetry breaking messengers axe in a simple form. The Standard Model is obtained after first step gauge symmetry breaking. In the case of one copy of the gauge interactions being strong, a scenario of electroweak symmetry breaking is discussed, and the gauginos are generally predicted to be heavier than the sfermions.
16420888
MeV tau neutrino in a gauge-mediated supersymmetry breaking model
A supersymmetric model which naturally accommodates MeV tau neutrinos within the framework of gauge-mediated supersymmetry breaking is described. The lepton number violation is originally introduced in the messenger sector of the theory. A large slepton-Higgs mixing mass and a small lepton-higgsino mixing mass are generated at one loop. The scalar tau neutrino has a non-vanishing vacuum expectation value. This results in a non-zero vτ mass which is in the range of 1–10 MeV.
15328619
Excited Heavy Mesons from QCD Sum Rules
Orbitally excited L=1 charm mesons are studied by QCD sum rules in the framework of heavy quark effective theory. The meson masses and the strong decay widths are obtained. This talk is based on our works of refs. 1 and 2 collaborated with Y.B. Dai, C.S. Huang, M.Q. Huang and H.Y. Jin.