The GL_2 main conjecture for elliptic curves without complex multiplication

The main conjectures of Iwasawa theory provide the only general method known at present for studying the mysterious relationship between purely arithmetic problems and the special values of complex L-functions, typified by the conjecture of Birch and Swinnerton-Dyer and its generalizations. Our goal in the present paper is to develop algebraic techniques which enable us to formulate a precise version of such a main conjecture for motives over a large class of p-adic Lie extensions of number fields. The paper ends by formulating and briefly discussing the main conjecture for an elliptic curve E over the rationals Q over the field generated by the coordinates of its p-power division points, where p is a prime greater than 3 of good ordinary reduction for E.Comment: 39 page

Interpolation between the epsilon and p regimes

We reconsider chiral perturbation theory in a finite volume and develop a new computational scheme which smoothly interpolates the conventional epsilon and p regimes. The counting rule is kept essentially the same as in the p expansion. The zero-momentum modes of Nambu-Goldstone bosons are, however, treated separately and partly integrated out to all orders as in the epsilon expansion. In this new scheme, the theory remains infra-red finite even in the chiral limit, while the chiral-logarithmic effects are kept present. We calculate the two-point function in the pseudoscalar channel and show that the correlator has a constant contribution in addition to the conventional hyperbolic cosine function of time t. This constant term rapidly disappears in the p regime but it is indispensable for a smooth convergence of the formula to the epsilon regime result. Our calculation is useful to precisely estimate the finite volume effects in lattice QCD simulations on the pion mass Mpi and kaon mass MK, as well as their decay constants Fpi and FK.Comment: 49 pages, 6 figures, minor corrections, references added, version to appear in PR

A20 deficiency sensitizes pancreatic beta cells to cytokine-induced apoptosis in vitro but does not influence type 1 diabetes development in vivo

SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Lattice study of meson correlators in the epsilon-regime of two-flavor QCD

We calculate mesonic two-point functions in the epsilon-regime of two-flavor QCD on the lattice with exact chiral symmetry. We use gauge configurations of size 16^3 32 at the lattice spacing a \sim 0.11 fm generated with dynamical overlap fermions. The sea quark mass is fixed at \sim 3 MeV and the valence quark mass is varied in the range 1-4 MeV, both of which are in the epsilon-regime. We find a good consistency with the expectations from the next-to-leading order calculation in the epsilon-expansion of (partially quenched) chiral perturbation theory. From a fit we obtain the pion decay constant F=87.3(5.6) MeV and the chiral condensate Sigma^{MS}=[239.8(4.0) MeV ]^3 up to next-to-next-to-leading order contributions.Comment: 20 pages, 12 figures, final version to appear in PR

Topology conserving gauge action and the overlap-Dirac operator

We apply the topology conserving gauge action proposed by Luescher to the four-dimensional lattice QCD simulation in the quenched approximation. With this gauge action the topological charge is stabilized along the hybrid Monte Carlo updates compared to the standard Wilson gauge action. The quark potential and renormalized coupling constant are in good agreement with the results obtained with the Wilson gauge action. We also investigate the low-lying eigenvalue distribution of the hermitian Wilson-Dirac operator, which is relevant for the construction of the overlap-Dirac operator.Comment: 27pages, 11figures, accepted versio

Holomorphic potentials for graded D-branes

We discuss gauge-fixing, propagators and effective potentials for topological A-brane composites in Calabi-Yau compactifications. This allows for the construction of a holomorphic potential describing the low-energy dynamics of such systems, which generalizes the superpotentials known from the ungraded case. Upon using results of homotopy algebra, we show that the string field and low energy descriptions of the moduli space agree, and that the deformations of such backgrounds are described by a certain extended version of `off-shell Massey products' associated with flat graded superbundles. As examples, we consider a class of graded D-brane pairs of unit relative grade. Upon computing the holomorphic potential, we study their moduli space of composites. In particular, we give a general proof that such pairs can form acyclic condensates, and, for a particular case, show that another branch of their moduli space describes condensation of a two-form.Comment: 47 pages, 7 figure

Vanishing cycles and mutation

This is the writeup of a talk given at the European Congress of Mathematics, Barcelona. It considers Picard-Lefschetz theory from the Floer cohomology viewpoint.Comment: 20 pages, LaTeX2e. TeXnical problem should now be fixed, so that the images will appear even if you download the .ps fil