16224921
On K3-Thurston 7-manifolds and their deformation space: A case study with remarks on general K3T and M-theory compactification
M-theory suggests the study of 11-dimensional space-times compactified on some 7-manifolds. From its intimate relation to superstrings, one possible class of such 7-manifolds are those that have Calabi-Yau threefolds as boundary. In this article, we construct a special class of such 7-manifolds, named as {\it K3-Thurston} (K3T) 7-manifolds. The factor from the K3 part of the deformation space of these K3T 7-manifolds admits a K\"{a}hler structure, while the factor of the deformation space from the Thurston part admits a special K\"{a}hler structure. The latter rings with the nature of the scalar manifold of a vector multiplet in an N=2 $d=4$ supersymmetric gauge theory. Remarks and examples on more general K3T 7-manifolds and issues to possible interfaces of K3T to M-theory are also discussed.
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.
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
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.
124850278
Decay Widths of Excited Heavy Mesons from Quantum Chromodynamics Sum Rules in the Infinite Mass Limit
The widths for pionic decays of the lowest two excited doublets (0(+), 1(+)) and (1(+), 2(+)) of heavy mesons are studied with quantum Chromodynamics sum rules in the heavy quark effective theory. The interpolating currents used allow us to distinguish the two 1(+) states without contamination in the infinite mass Limit. The soft pion approximation is not used in the calculations.
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.
2525683
Two particle states in an asymmetric box
The exact two-particle energy eigenstates in an asymmetric rectangular box with periodic boundary conditions in all three directions are studied. Their relation with the elastic scattering phases of the two particles in the continuum are obtained. These results can be viewed as a generalization of the corresponding formulae in a cubic box obtained by Luscher before. In particular, the s-wave scattering length is related to the energy shift in the finite box. Possible applications of these formulae are also discussed.
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.
14127649
Recent Lifetime and Mixing Measurements at the Tevatron
We present the latest $B$ hadron lifetimes, $B^0_s$ mixing, and $D^0$ mixing measurements using up to 3.0 fb$^{-1}$ of data collected by CDF and D0 experiments at Fermilab. The $B^0_s$ lifetime is measured from both $J/\psi \phi$ (CP admixture) and flavor specific channels, and the $B_c$ lifetime is obtained from semileptonic channels. Following the $B^0_s$ oscillation frequency measurement at CDF in 2006, the D0 collaboration now observes $B^0_s$ oscillation at a significance of about 3$\sigma$. Since the first $D^0$ mixing evidence established at $B$ factories in 2007, CDF has observed $D^0$ mixing at a significance of about 4$\sigma$ level, the first time from hadron collider.