14173643
On the global structure of some natural fibrations of Joyce manifolds
The study of fibrations of the target manifolds of string/M/F-theories has provided many insights to the dualities among these theories or even as a tool to build up dualities since the work of Strominger, Yau, and Zaslow on the Calabi-Yau case. For M-theory compactified on a Joyce manifold M 7 , the fact that M 7 is constructed via a generalized Kummer construction on a 7-torus T 7 with a torsion-free G2-structure ϕ suggests that there are natural fibrations of M 7 by T 3 , T 4 , and K3 surfaces in a way governed by ϕ. The local picture of some of these fibrations and their roles in dualities between string/M-theory have been studied intensively in the work of Acharya. In this present work, we explain how one can understand their global and topological details in terms of bundles over orbifolds. After the essential background is provided in Sec. 1, we give general discussions in Sec. 2 about these fibrations, their generic and exceptional fibers, their monodromy, and the base orbifolds. Based on these, one obtains a 5-step-routine to understand the fibrations, which we illustrate by examples in Sec. 3. In Sec. 4, we turn to another kind of fibrations for Joyce manifolds, namely the fibrations by the Calabi-Yau threefolds constructed by Borcea and Voisin. All these fibrations arise freely and naturally from the work of Joyce. Understanding how the global structure of these fibrations may play roles in string/M-theory duality is one of the major issues for further pursuit.
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.
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.
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.
119251181
Understanding Ultracold Neutron Production in Oxygen Solids from Volume and Temperature Dependent Yields
We present experimental data on ultracold neutron (UCN) production in solid oxygen from 5 K to 50 K. The experiment used 3 cells of different dimensions in order to study the excess UCN elastic scattering in s-O$_2$ due to source density non-uniformities. We present a combined $\chi^2$ analysis with the aid of Monte-Carlo simulations which contain the detailed physics of UCN transport as well as cold neutron attenuation. The results validate the UCN production and upscattering cross-sections extracted from the dynamic structure function derived from inelastic neutron scattering, and illustrate the role of magnetic scattering in enhancing UCN production in s-O$_2$.
15819599
Spectral Parameters and Spectral Weights of Unstable Particles in Lattice QCD
We discuss the issues related to the spectral parameters (mass and width) of unstable particles in lattice calculations. Using a solvable model, the Lee Model, we show that the eigenvalues of the Hamiltonian, which is the spectrum measured from the Euclidean correlation functions in lattice simulations, need not be the same as the energy at which the scattering phase passes through π/2. It is in general also different from the real part of the actual pole position for the S-matrix element. These three quantities are close to one another only when the resonance is narrow. We also investigate the volume dependence of the so-called spectral weights for the energy eigenstates which can be obtained in lattice simulations. The volume dependence of this quantity helps to distinguish between one-particle and two-particle states in lattice calculations. Within the Lee model, we verify that this is indeed the case when the so-called V -particle is stable. For an unstable V -particle (resonance), this method is only applicable for narrow resonances. We argue that this conclusion should also be qualitatively correct in general theories like QCD.
14564909
Stau LSP and comparison with H+- phenomenology
In supersymmetric models with explicit breaking of R parity the lightest supersymmetric particle (LSP) may be the lightest stau (τ) over tilde (1). Such a scenario would provide a clear sign of R-parity violating SUSY, although its phenomenology may resemble that of a charged Higgs boson H+/-. We discuss various ways of distinguishing a LSP (τ) over tilde (1) from H+/- at future colliders, and address the case of (τ) over tilde (1) mimicking the signal for H+/-. As an example we suggest that the recent L3 signal for H+H--->qq' qq' and H+H- --> qq' taunu(tau) could be more easily explained by a LSP (τ) over tilde (1).
119214299
Effect of an electric field on superfluid helium scintillation produced by $\alpha$-particle sources
We report a study of the intensity and time dependence of scintillation produced by weak alpha particle sources in superfluid helium in the presence of an electric field (0 - 45 kV/cm) in the temperature range of 0.2 K to 1.1 K at the saturated vapor pressure. Both the prompt and the delayed components of the scintillation exhibit a reduction in intensity with the application of an electric field. The reduction in the intensity of the prompt component is well approximated by a linear dependence on the electric field strength with a reduction of 15% at 45 kV/cm. When analyzed using the Kramers theory of columnar recombination, this electric field dependence leads to the conclusion that roughly 40% of the scintillation results from species formed from atoms originally promoted to excited states and 60% from excimers created by ionization and subsequent recombination with the charges initially having a cylindrical Gaussian distribution about the alpha track of 60 nm radius. The intensity of the delayed component of the scintillation has a stronger dependence on the electric field strength and on temperature. The implications of these data on the mechanisms affecting scintillation in liquid helium are discussed.
124563066
Baryonic Isgur-Wise functions in large-N-c heavy quark effective theory
Large-N-c relations among baryonic Isgur-Wise functions appearing at the order of 1/m(Q) are analyzed. An application to Omega(b) -> Omega(c) weak decays is given.