15974050
Transformation of algebraic Gromov-Witten invariants of three-folds under flops and small extremal transitions, with an appendix from the stringy and the symplectic viewpoint
We study how Gromov-Witten invariants of projective 3-folds transform under a standard flop and a small extremal transition in the algebro-geometric setting from the recent development of algebraic relative Gromov-Witten theory and its applications. This gives an algebro-geometric account of Witten’s wall-crossing formula for correlation functions of the descendant nonlinear sigma model in adjacent geometric phases of a gauged linear sigma model and of the symplectic approach in an earlier work of An-Min Li and Yongbin Ruan on the same problem. A terse account from the stringy and the symplectic viewpoint is given in the appendix to complement and compare to the discussion in the main text.
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.
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
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.
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.
121803018
PRELIMINARY RESULTS FOR LIGHT HADRON MASSES FROM LATTICE QCD ON ASYMMETRIC LATTICES
1482312
Strongly interacting Higgs sector without technicolor
Simulation results are presented on Higgs mass calculations in the spontaneously broken phase of the Higgs sector in the minimal Standard Model with a higher derivative regulator. A heavy Higgs particle is found in the TeV mass range in the presence of a complex conjugate ghost pair at higher energies. The ghost pair evades easy experimental detection. As a finite and unitary theory in the continuum, this model serves as an explicit and simple example of a strongly interacting Higgs sector without technicolor.
20143159
Measurements of ultracold-neutron lifetimes in solid deuterium.
We present the first measurements of the survival time of ultracold neutrons (UCNs) in solid deuterium (SD2). This critical parameter provides a fundamental limitation to the effectiveness of superthermal UCN sources that utilize solid ortho-deuterium as the source material. These measurements are performed utilizing a SD2 source coupled to a spallation source of neutrons, providing a demonstration of UCN production in this geometry and permitting systematic studies of the influence of thermal up-scatter and contamination with para-deuterium on the UCN survival time.
119447810
Note on the slope parameter of the baryonic Lambda(b) ---> Lambda(c) Isgur-Wise function
Abstract Using the framework of the Heavy Quark Effective Theory we have re-analyzed the Isgur–Wise function describing semileptonic Λ b → Λ c decays in the QCD sum rule approach. The slope parameter of the Isgur–Wise function is found to be ρ 2 = 1.35 ± 0.13 , which is consistent with an experimental measurement and a lattice calculation. To O ( 1 / m b , 1 / m c ) of the heavy quark expansion the integrated Λ b decay width is used to extract the CKM matrix element V c b for which we obtain a value of | V c b | = 0.041 ± 0.004 ± 0.001 in excellent agreement with the value of | V c b | determined from semileptonic B → D ∗ decays.