Renormalon disappearance in Borel sum of the 1/N expansion of the Gross-Neveu model mass gap

The exact mass gap of the O(N) Gross-Neveu model is known, for arbitrary $N$, from non-perturbative methods. However, a "naive" perturbative expansion of the pole mass exhibits an infinite set of infrared renormalons at order 1/N, formally similar to the QCD heavy quark pole mass renormalons, potentially leading to large ${\cal O}(\Lambda)$ perturbative ambiguities. We examine the precise vanishing mechanism of such infrared renormalons, which avoids this (only apparent)contradiction, and operates without need of (Borel) summation contour prescription, usually preventing unambiguous separation of perturbative contributions. As a consequence we stress the direct Borel summability of the (1/N) perturbative expansion of the mass gap. We briefly speculate on a possible similar behaviour of analogous non-perturbative QCD quantities.Comment: 16 pp., 1 figure. v2: a few paragraphs and one appendix added, title and abstract slightly changed, essential results unchange

c=rgc = r_g Theories of WGW_G-Gravity: The Set of Observables as a Model of Simply Laced GG

We propose to study a generalization of the Klebanov-Polyakov-Witten (KPW) construction for the algebra of observables in the $c = 1$ string model to theories with $c > 1$. We emphasize the algebraic meaning of the KPW construction for $c = 1$ related to occurrence of a {\it model} of {\it SU}(2) as original structure on the algebra of observables. The attempts to preserve this structure in generalizations naturally leads to consideration of $W$-gravities. As a first step in the study of these generalized KPW constructions we design explicitly the subsector of the space of observables in appropriate $W_G$-string theory, which forms the {\it model} of $G$ for any simply laced {\it G}. The {\it model} structure is confirmed by the fact that corresponding one-loop Kac-Rocha-Caridi $W_G$-characters for $c = r_G$ sum into a chiral (open string) $k=1$ $G$-WZW partition function.Comment: 36

A Branched Kinetic Scheme Describes the Mechanochemical Coupling of Myosin Va Processivity in Response to Substrate

Myosin Va is a double-headed cargo-carrying molecular motor that moves processively along cellular actin filaments. Long processive runs are achieved through mechanical coordination between the two heads of myosin Va, which keeps their ATPase cycles out of phase, preventing both heads detaching from actin simultaneously. The biochemical kinetics underlying processivity are still uncertain. Here we attempt to define the biochemical pathways populated by myosin Va by examining the velocity, processive run-length, and individual steps of a Qdot-labeled myosin Va in various substrate conditions (i.e., changes in ATP, ADP, and Pi) under zero load in the single-molecule total internal reflection fluorescence microscopy assay. These data were used to globally constrain a branched kinetic scheme that was necessary to fit the dependences of velocity and run-length on substrate conditions. Based on this model, myosin Va can be biased along a given pathway by changes in substrate concentrations. This has uncovered states not normally sampled by the motor, and suggests that every transition involving substrate binding and release may be strain-dependent. © 2012 Biophysical Society

Non-Abelian Magnetized Blackholes and Unstable Attractors

Fluctuations of non-Abelian gauge fields in a background magnetic flux contain tachyonic modes and hence the background is unstable. We extend these results to the cases where the background flux is coupled to Einstein gravity and show that the corresponding spherically symmetric geometries, which in the absence of a cosmological constant are of the form of Reissner-Nordstrom blackholes or the AdS_2xS^2, are also unstable. We discuss the relevance of these instabilities to several places in string theory including various string compactifications and the attractor mechanism. Our results for the latter imply that the attractor mechanism shown to work for the extremal Abelian charged blackholes, cannot be applied in a straightforward way to the extremal non-Abelian colored blackholes.Comment: 23 pages, 3 .eps figures; v2: Stability of minimal charge blackhole emphasized, Refs adde

New Criticality of 1D Fermions

One-dimensional massive quantum particles (or 1+1-dimensional random walks) with short-ranged multi-particle interactions are studied by exact renormalization group methods. With repulsive pair forces, such particles are known to scale as free fermions. With finite $m$-body forces (m = 3,4,...), a critical instability is found, indicating the transition to a fermionic bound state. These unbinding transitions represent new universality classes of interacting fermions relevant to polymer and membrane systems. Implications for massless fermions, e.g. in the Hubbard model, are also noted. (to appear in Phys. Rev. Lett.)Comment: 10 pages (latex), with 2 figures (not included

(Borel) convergence of the variationally improved mass expansion and the O(N) Gross-Neveu model mass gap

We reconsider in some detail a construction allowing (Borel) convergence of an alternative perturbative expansion, for specific physical quantities of asymptotically free models. The usual perturbative expansions (with an explicit mass dependence) are transmuted into expansions in 1/F, where $F \sim 1/g(m)$ for $m \gg \Lambda$ while $F \sim (m/\Lambda)^\alpha$ for m \lsim \Lambda, $\Lambda$ being the basic scale and $\alpha$ given by renormalization group coefficients. (Borel) convergence holds in a range of $F$ which corresponds to reach unambiguously the strong coupling infrared regime near $m\to 0$, which can define certain "non-perturbative" quantities, such as the mass gap, from a resummation of this alternative expansion. Convergence properties can be further improved, when combined with $\delta$ expansion (variationally improved perturbation) methods. We illustrate these results by re-evaluating, from purely perturbative informations, the O(N) Gross-Neveu model mass gap, known for arbitrary $N$ from exact S matrix results. Comparing different levels of approximations that can be defined within our framework, we find reasonable agreement with the exact result.Comment: 33 pp., RevTeX4, 6 eps figures. Minor typos, notation and wording corrections, 2 references added. To appear in Phys. Rev.

Quantum Field Theory in the Large N Limit: a review

We review the solutions of O(N) and U(N) quantum field theories in the large $N$ limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large $N$, the method relies on constructing effective field theories for composite fields after integration over the original degrees of freedom. We first solve a general scalar U(\phib^2) field theory for $N$ large and discuss various non-perturbative physical issues such as critical behaviour. We show how large $N$ results can also be obtained from variational calculations.We illustrate these ideas by showing that the large $N$ expansion allows to relate the (\phib^2)^2 theory and the non-linear $\sigma$-model, models which are renormalizable in different dimensions. Similarly, a relation between $CP(N-1)$ and abelian Higgs models is exhibited. Large $N$ techniques also allow solving self-interacting fermion models. A relation between the Gross--Neveu, a theory with a four-fermi self-interaction, and a Yukawa-type theory renormalizable in four dimensions then follows. We discuss dissipative dynamics, which is relevant to the approach to equilibrium, and which in some formulation exhibits quantum mechanics supersymmetry. This also serves as an introduction to the study of the 3D supersymmetric quantum field theory. Large $N$ methods are useful in problems that involve a crossover between different dimensions. We thus briefly discuss finite size effects, finite temperature scalar and supersymmetric field theories. We also use large $N$ methods to investigate the weakly interacting Bose gas. The solution of the general scalar U(\phib^2) field theory is then applied to other issues like tricritical behaviour and double scaling limit.Comment: Review paper: 200 pages, 13 figure

Agriculture in the Face of Changing Markets, Institutions and Policies: Challenges and Strategies

Since the late 1980s, agriculture in Central and Eastern European Countries (CEECs) has been under considerable adjustment pressure due to changing political, economic and institutional environments. These changes have been linked to the transition process, as well as the ongoing integration into the European Union and the world market. Reduced subsidies, increased environmental and food quality demands, as well as structural changes in the supply, processing and food retailing sector call for major structural adjustments and the improvement of farmersâ managerial abilities. Though such changes always carry significant threats to farms, they also offer new opportunities for the farms' entrepreneurial engagement. Upcoming changes in the agricultural environment and their possible consequences for farm structures across Europe are thus still timely subjects. The objective of the IAMO Forum 2006 is to contribute to the success of agriculture in the CEECs, as well as their neighboring countries, in todayâs increasingly competitive environment. Concrete questions the conference focuses on are: What are the most suitable farm organizations, cooperative arrangements and contractual forms? How to improve efficiency and productivity? Where do market niches lie and what are the new product demands? This book contains 33 invited and selected contributions. These papers will be presented at the IAMO Forum 2006 in order to offer a platform for scientists, practitioners and policy-makers to discuss challenges and potential strategies at the farm, value chain, rural society and policy levels in order to cope with the upcoming challenges. IAMO Forum 2006, as well as this book, would not have been possible without the engagement of many people and institutions. We thank the authors of the submitted abstracts and papers, as well as the referees, for their evaluation of the abstracts from which the papers were selected. In particular, we would like to express our thanks to OLIVER JUNGKLAUS, GABRIELE MEWES, KLAUS REINSBERG and ANGELA SCHOLZ, who significantly contributed to the organization of the Forum. Furthermore, our thanks goes to SILKE SCHARF for her work on the layout and editing support of this book, and to JIM CURTISS, JAMIE BULLOCH, and DÃNALL Ã MEARÃIN for their English proof-reading. As experience from previous years documents, the course of the IAMO Forum continues to profit from the support and engagement of the IAMO administration, which we gratefully acknowledge. Last but not least, we are very grateful to the Robert Bosch Foundation, the Federal Ministry of Nutrition, Agriculture and Consumer Protection (BMELV), the German Research Foundation (DFG), the Haniel Foundation and the Leibniz Institute of Agricultural Development in Central and Eastern Europe (IAMO) for their respective financial support.Agribusiness, Community/Rural/Urban Development, Farm Management, Industrial Organization, International Development, Labor and Human Capital, Land Economics/Use, Productivity Analysis,

Vortices, Instantons and Branes

The purpose of this paper is to describe a relationship between the moduli space of vortices and the moduli space of instantons. We study charge k vortices in U(N) Yang-Mills-Higgs theories and show that the moduli space is isomorphic to a special Lagrangian submanifold of the moduli space of k instantons in non-commutative U(N) Yang-Mills theories. This submanifold is the fixed point set of a U(1) action on the instanton moduli space which rotates the instantons in a plane. To derive this relationship, we present a D-brane construction in which the dynamics of vortices is described by the Higgs branch of a U(k) gauge theory with 4 supercharges which is a truncation of the familiar ADHM gauge theory. We further describe a moduli space construction for semi-local vortices, lumps in the CP(N) and Grassmannian sigma-models, and vortices on the non-commutative plane. We argue that this relationship between vortices and instantons underlies many of the quantitative similarities shared by quantum field theories in two and four dimensions.Comment: 32 Pages, 4 Figure

Mapping the physiography of Michigan with GIS

Abstract: We present a new physiographic map of Michigan, that is also available interactively, online. Only four, small-scale physiographic maps of Michigan had been previously published. Our mapping project made use of a wide variety of spatial data, in a GIS environment, to visualize and delineate the physical landscape in more detail than has been done previously. We also examined many of the unit boundaries in the field, using a GIS running on a GPS-enabled laptop. Unlike previous physiographic maps, the online version of the map enables users to query the criteria used to define each of the 224 boundaries of its 10 major and 91 minor physiographic units. The interactive nature of the online version of the map is a unique enhancement to physiographic maps and mapping. Our study also provides data on the number and types of criteria used to define each of the 224 unit boundaries within the map. Most of our unit boundaries are based on data derived from 10-m raster elevation data and NRCS soils data, e.g., relief, soil wetness, escarpments, landscape fabric, and parent material characteristics. Data gleaned from NRCS SSURGO county-scale soil maps were a strength of the project