16892624
Azumaya structure on D-branes and deformations and resolutions of a conifold revisited: Klebanov-Strassler-Witten vs. Polchinski-Grothendieck
In this sequel to [L-Y1], [L-L-S-Y], and [L-Y2] (respectively arXiv:0709.1515 [math.AG], arXiv:0809.2121 [math.AG], and arXiv:0901.0342 [math.AG]), we study a D-brane probe on a conifold from the viewpoint of the Azumaya structure on D-branes and toric geometry. The details of how deformations and resolutions of the standard toric conifold Y can be obtained via morphisms from Azumaya points are given. This should be compared with the quantum-field-theoretic/D-brany picture of deformations and resolutions of a conifold via a D-brane probe sitting at the conifold singularity in the work of Klebanov and Witten [K-W] (arXiv:hep-th/9807080) and Klebanov and Strasser [K-S] (arXiv:hep-th/0007191). A comparison with resolutions via noncommutative desingularizations is given in the end.
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
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.
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.
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.
16041460
Intermediate scale dependence of non-universal gaugino masses in supersymmetric SO(10)
We calculate the dependence on the intermediate scale of the gaugino mass ratios upon breaking of SO(10) into the standard model via an intermediate group H. We see that the ratios change significantly when the intermediate scale is low (say, 10(8) GeV or 1 TeV) compared to the case when the two breakings occur at the same scale.
119368335
The Higgs model with a complex ghost pair
Abstract A higher derivative term is introduced in the kinetic energy of the Higgs lagrangian in the minimal Standard Model. A logically consistent and finite field theory is obtained when some excitations of the Higgs field are quantized with indefinite metric in the Hilbert space. The Landau ghost phenomenon of the ponventional triviality problem is replaced by the state vectors of a complex ghost pair at a finite mass scale with observable physical consequences. It is shown that the ghost states exhibit unusual resonance properties and correspond to a complex conjugate pair of Pauli-Villars regulator masses in the euclidean path integral formulation of the theory. An argument is given that microscopic acausality effects associated with the ghost pair remain undetectable in scattering processes with realistic wave packets, and the S -matrix should exhibit unitarity in the observable sector of the Hilbert space.
118527003
Strong gravitational lensing of quasi-Kerr compact object with arbitrary quadrupole moments
A bstractWe study the strong gravitational lensing on the equatorial plane of a quasi-Kerr compact object with arbitrary quadrupole moments which can be used to model the super-massive central object of the galaxy. We find that, when the quadrupolar correction parameter ξ takes the positive (negative) value, the photon-sphere radius rps, the minimum impact parameter ups, the coefficient $ \overline b $, the relative magnitudes rm and the angular position of the relativistic images θ∞ are larger (smaller) than the results obtained in the Kerr black hole, but the coefficient $ \overline a $, the deflection angle α(θ) and the angular separation s are smaller (larger) than that in the Kerr black hole. These features may offer a way to probe special properties for some rotating compact objects by the astronomical instruments in the future.
120175902
A NEW SEARCH FOR A PERMANENT DIPOLE MOMENT OF THE ELECTRON IN A SOLID STATE SYSTEM
Measurements of the electric dipole moment (EDM) of the neutron and the electron put the most stringent constraints on new sources of CP violation. CP violation is essential for generating the observed baryon asymmetry of the universe (BAU). Many models which propose large CP-odd mechanisms for BAU predict EDMs that exceed the limits of the most sensitive measurements. We are conducting a high sensitivity search for the electron EDM using a solid state system. It promises orders of magnitude improvement over atomic beam experiments solely from the available electron density. We present the experimental design and report on the current status.
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.