117729451
Immersed Lagrangian deformations of a branched covering of a special Lagrangian 3-sphere in a Calabi-Yau 3-fold and its deviation from Joyce's criteria: Potential image-support rigidity of A-branes that wrap around a sL $S^3$
Using a hyperK\"{a}hler rotation on complex structures of a Calabi-Yau 2-fold and rolling of an isotropic 2-submanifold in a symplectic 6-manifold, we construct, by gluing, a natural family of immersed Lagrangian deformations of a branched covering of a special Lagrangian 3-sphere in a Calabi-Yau 3-fold and study how they deviate from being deformable to a family of special Lagrangian deformations by examining in detail Joyce's criteria on this family. The result suggests a potential image-support rigidity of A-branes that wrap around a special Lagrangian 3-sphere in a Calabi-Yau 3-fold, which resembles a similar phenomenon for holomorphic curves that wrap around a rigid smooth rational curve in a Calabi-Yau 3-fold in Gromov-Witten theory.
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.
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
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$_2$.
118963023
Strongly interacting Higgs sector in the minimal Standard Model
Abstract The triviality Higgs mass bound is studied with a higher derivative regulating in the spontaneously broken phase of the four dimensional O(4) symmetric scalar fiel-theory with quartic self-interaction. The phase diagram of the O(4) model is determined in a Monte Carlo simulation which interpolates between the hypercubic lattice regulator and the higher derivative regulator in continuum space-time. The same method can be used to calculate the Higgs mass bound in continuum space-time. In a large- N analysis, when compared with a hypercubic lattice, we find a relative increase in the triviality bound of the higher derivative regulator suggesting a strongly interacting Higgs sector in the TeV region with negligible dependence on regulator parameters. When the higher derivative regulator mass is brought close to the Higgs mass the model requires a more elaborate analysis of complex ghost states in scattering amplitudes.
119109295
Collision of two general geodesic particles around a Kerr-Newman black hole
We study collision of two general geodesic particles around the Kerr-Newman (KN) black hole and get the center-of-mass (CM) energy of the non-marginally and marginally bound critical particles in the direct collision and LSO collision scenarios. We find the constraint conditions that arbitrarily high CM energy can be obtained for the near-horizon collision of two general geodesic particles in the extremal KN black hole, and note that the charge decreases the value of the latitude in which arbitrarily high CM energy can occurs. We also interpret why the high-velocity collision belt centers to the equator with the increase of the charge.
121774503
Volume dependence of spectral weight functions
It has been suggested that the volume dependence of the spectral weight could be utilized as a probe to distinguish single and multiparticle states in Monte Carlo simulations. In a recent study using a solvable model, the Lee model, we found that this criteria is not applicable for broad resonances. In this paper, the same question is addressed within the finite-size formalism outlined by Luescher. A similar conclusion has been reached. This is first studied using a quantum-mechanical scattering model. Then, following analogous arguments as in the original Luescher's formalism, the result is generalized to massive quantum field theories under the same conditions as the conventional Luescher's formulas. A possibility of extracting resonance parameters using the spectral weight function is also pointed out.
14722253
STATIC QUARK POTENTIAL AND THE RENORMALIZED ANISOTROPY ON TADPOLE IMPROVED ANISOTROPIC LATTICES
Static quark potential is studied using a tadpole improved gauge lattice action. The scale is set using the potential for a wide range of bare parameters. The renormalized anisotropy of the lattice is also measured.