18139263
On A-twisted moduli stack for curves from Witten's gauged linear sigma models
Witten’s gauged linear sigma model [Wi1] is one of the universal frameworks or structures that lie behind stringy dualities. Its A-twisted moduli space at genus 0 case has been used in the Mirror Principle [L-L-Y] that relates Gromov-Witten invariants and mirror symmetry computations. In this paper the A-twisted moduli stack for higher genus curves is defined and systemically studied. It is proved that such a moduli stack is an Artin stack. For genus 0, it has the A-twisted moduli space of [MP] as the coarse moduli space. The detailed proof of the regularity of the collapsing morphism by Jun Li in [L-L-Y: I and II] can be viewed as a natural morphism from the moduli stack of genus 0 stable maps to the A-twisted moduli stack at genus 0. Due to the technical demand of stacks to physicists and the conceptual demand of supersymmetry to mathematicians, a brief introduction of each topic that is most relevant to the main contents of this paper is given in the beginning and the appendix respectively. Themes for further study are listed in the end.
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.
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.
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.
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.
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
119251998
On Supersymmetries
After reviewing electroweak (EW) scale supersymmetry (susy) and split susy, as well as their implications in very high energy cosmic rays, I present a high scale susy model for fermion masses. An O(0.1) nu_e-nu_{tau} mixing is expected.
5304169
A high dynamic range data acquisition system for a solid-state electron electric dipole moment experiment.
We have built a high precision (24-bit) data acquisition (DAQ) system capable of simultaneously sampling eight input channels for the measurement of the electric dipole moment of the electron. The DAQ system consists of two main components: a master board for DAQ control and eight individual analog-to-digital converter (ADC) boards for signal processing. This custom DAQ system provides galvanic isolation of the ADC boards from each other and the master board using fiber optic communication to reduce the possibility of ground loop pickup and attain ultimate low levels of channel cross-talk. In this paper, we describe the implementation of the DAQ system and scrutinize its performance.
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.
14586429
QCD sum rule analysis for the Lambda(b)->Lambda(c) semileptonic decay
Abstract The 1 m c and 1 m b corrections to the Λ b → Λ c semileptonic decay are analyzed by QCD sum rules. Within the framework of heavy quark effective theory, the subleading baryonic Isgur-Wise function of Λ b → Λ c has been calculated. It is shown that the corrections due to the 1 m Lagrangian insertion are negligibly small. The sizable 1 m Q effect to the decay lies only in the weak current. The decay spectrum and the branching ratio are given.
118375342
Supersymmetric extension of the minimal dark matter model
The minimal dark matter model is given a supersymmetric extension. A super SU(2)(L) quintuplet is introduced with its fermionic neutral component still being the dark matter, and the dark matter mass is about 19.7 TeV. Mass splitting among the quintplet due to supersymrnetry particles is found to be negligibly small compared to the electroweak corrections. Other properties of this supersymmetry model are studied, it has the solutions to the PAMELA and Fermi-LAT anomaly, and the predictions in higher energies need further experimental data to verify them.