Categories of holomorphic line bundles on higher dimensional noncommutative complex tori

We construct explicitly noncommutative deformations of categories of holomorphic line bundles over higher dimensional tori. Our basic tools are Heisenberg modules over noncommutative tori and complex/holomorphic structures on them introduced by A. Schwarz. We obtain differential graded (DG) categories as full subcategories of curved DG categories of Heisenberg modules over the complex noncommutative tori. Also, we present the explicit composition formula of morphisms, which in fact depends on the noncommutativity.Comment: 28 page

Star product formula of theta functions

As a noncommutative generalization of the addition formula of theta functions, we construct a class of theta functions which are closed with respect to the Moyal star product of a fixed noncommutative parameter. These theta functions can be regarded as bases of the space of holomorphic homomorphisms between holomorphic line bundles over noncommutative complex tori.Comment: 12 page

Electronic mean free path in as-produced and purified single-wall carbon nanotubes

The effect of purification on room temperature electronic transport properties of single-wall carbon nanotubes (SWNT) was studied by submerging samples into liquid mercury. The conductance plots of purified SWNTs showed plateaus, indicating weak dependence of the electrical resistance on the length of the tube connecting the electrodes, providing evidence of quasi-ballistic conduction in SWNTs. The electronic mean free path of the purified SWNTs reached a few microns, which is longer than that of the as-produced SWNTs, and which is consistent with the calculation based on the scattering by acoustic phonons

Live imaging of whole mouse embryos during gastrulation : migration analyses of epiblast and mesodermal cells

During gastrulation in the mouse embryo, dynamic cell movements including epiblast invagination and mesodermal layer expansion lead to the establishment of the three-layered body plan. The precise details of these movements, however, are sometimes elusive, because of the limitations in live imaging. To overcome this problem, we developed techniques to enable observation of living mouse embryos with digital scanned light sheet microscope (DSLM). The achieved deep and high time-resolution images of GFP-expressing nuclei and following 3D tracking analysis revealed the following findings: (i) Interkinetic nuclear migration (INM) occurs in the epiblast at embryonic day (E)6 and 6.5. (ii) INM-like migration occurs in the E5.5 embryo, when the epiblast is a monolayer and not yet pseudostratified. (iii) Primary driving force for INM at E6.5 is not pressure from neighboring nuclei. (iv) Mesodermal cells migrate not as a sheet but as individual cells without coordination

Quantum Open-Closed Homotopy Algebra and String Field Theory

We reformulate the algebraic structure of Zwiebach's quantum open-closed string field theory in terms of homotopy algebras. We call it the quantum open-closed homotopy algebra (QOCHA) which is the generalization of the open-closed homotopy algebra (OCHA) of Kajiura and Stasheff. The homotopy formulation reveals new insights about deformations of open string field theory by closed string backgrounds. In particular, deformations by Maurer Cartan elements of the quantum closed homotopy algebra define consistent quantum open string field theories.Comment: 36 pages, fixed typos and small clarifications adde

On open-closed extension of boundary string field theory

We investigate a classical open-closed string field theory whose open string sector is given by boundary string field theory. The open-closed interaction is introduced by the overlap of a boundary state with a closed string field. With the help of the Batalin-Vilkovisky formalism, the closed string sector is determined to be the HIKKO closed string field theory. We also discuss the gauge invariance of this theory in both open and closed string sides.Comment: 25 pages, 2 figures, comments and a reference added, typos correcte

BFV-complex and higher homotopy structures

We present a connection between the BFV-complex (abbreviation for Batalin-Fradkin-Vilkovisky complex) and the so-called strong homotopy Lie algebroid associated to a coisotropic submanifold of a Poisson manifold. We prove that the latter structure can be derived from the BFV-complex by means of homotopy transfer along contractions. Consequently the BFV-complex and the strong homotopy Lie algebroid structure are $L_{\infty}$ quasi-isomorphic and control the same formal deformation problem. However there is a gap between the non-formal information encoded in the BFV-complex and in the strong homotopy Lie algebroid respectively. We prove that there is a one-to-one correspondence between coisotropic submanifolds given by graphs of sections and equivalence classes of normalized Maurer-Cartan elemens of the BFV-complex. This does not hold if one uses the strong homotopy Lie algebroid instead.Comment: 50 pages, 6 figures; version 4 is heavily revised and extende

Unstable solitons on noncommutative tori and D-branes

We describe a class of exact solutions of super Yang-Mills theory on even-dimensional noncommutative tori. These solutions generalize the solitons on a noncommutative plane introduced in hep-th/0009142 that are conjectured to describe unstable D2p-D0 systems. We show that the spectrum of quadratic fluctuations around our solutions correctly reproduces the string spectrum of the D2p-D0 system in the Seiberg-Witten decoupling limit. In particular the fluctuations correctly reproduce the 0-0 string winding modes. For p=1 and p=2 we match the differences between the soliton energy and the energy of an appropriate SYM BPS state with the binding energies of D2-D0 and D4-D0 systems. We also give an example of a soliton that we conjecture describes branes of intermediate dimension on a torus such as a D2-D4 system on a four-torus.Comment: 22 pages, Latex; v.2: references adde

Boundary states, matrix factorisations and correlation functions for the E-models

The open string spectra of the B-type D-branes of the N=2 E-models are calculated. Using these results we match the boundary states to the matrix factorisations of the corresponding Landau-Ginzburg models. The identification allows us to calculate specific terms in the effective brane superpotential of E_6 using conformal field theory methods, thereby enabling us to test results recently obtained in this context.Comment: 20 pages, no figure