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.
116912536
Algebraic cobordism of filtered vector bundles on varieties: Notes on a work of Lee and Pandharipande
The construction of double point cobordism groups of vector bundles on varieties in the work [Lee-P] (arXiv:1002.1500 [math.AG]) of Yuan-Pin Lee and Rahul Pandharipande gives immediately double point cobordism groups of filtered vector bundles on varieties. We note also that among the four basic operations – direct sum, tensor product, dual, and Hom – on vector bundles on varieties, only taking dual is compatible with double point cobordisms of vector bundles on varieties in general, by a demonstration on an example of vector bundles on Calabi-Yau 3-folds. A question on refined and/or higher algebraic cobordisms of vector bundles on varieties is posed in the end.
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.
17146622
Toric morphisms and fibrations of toric Calabi-Yau hypersurfaces
Special fibrations of toric varieties have been used by physicists, e.g. the school of Candelas, to construct dual pairs in the study of Het/F-theory duality. Motivated by this, we investigate in this paper the details of toric morphisms between toric varieties. In particular, a complete toric description of fibers - both generic and non-generic -, image, and the flattening stratification of a toric morphism are given. Two examples are provided to illustrate the discussions. We then turn to the study of the restriction of a toric morphism to a toric hypersurface. The details of this can be understood by the various restrictions of a line bundle with a section that defines the hypersurface. These general toric geometry discussions give rise to a computational scheme for the details of a toric morphism and the induced fibration of toric hypersurfaces therein. We apply this scheme to study the family of 4-dimensional elliptic Calabi-Yau toric hypersurfaces that appear in a recent work of Braun-Candelas-dlOssa-Grassi. The Maple codes that are employed for the computation are provided. Some directions for future work 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.
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
119216988
LHCb $\bigtriangleup A_{CP}$ of $D$ Meson and R-Parity Violation
LHCb collaboration has recently announced a measurement of the difference of time-integrated CP asymmetries between $D\rightarrow K^+K^-$ and $D \rightarrow \pi^+\pi^-$. This result provides the evidence of large direct CP violation in $D$ meson and reveals some important implications on underlying new physics. It is shown that the direct CP violation in $D$ meson can be enhanced by R-parity violating supersymmetry, while CP violations in $K$ and $B$ mesons are suppressed by this new physics, which is in consistence with previous experiments. Constraints on the model parameters and some consequences are also discussed.
14087435
Determination of the Free Neutron Lifetime
We present the status of current US experimental efforts to measure the lifetime of the free neutron by the "beam" and "bottle" methods. BBN nucleosynthesis models require accurate measurements with 1 second uncertainties, which are currently feasible. For tests of physics beyond the standard model, future efforts will need to achieve uncertainties well below 1 second. We outline paths achieve both.
118538966
Review of D Semi-leptonic Decays
Semi-leptonic D decays continue to play an important role in the field of flavor physics. During this presentation, recent measurements from pseudo-scalar to pseudo-scalar modes, pseudo-scalar to vector modes, and rare modes will be discussed. These results are important for many purposes, such as validating the machinery of lattice QCD, extracting CKM matrix elements, and searching for new physics and new interactions.
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.
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$_2$.