On the zero of the fermion zero mode

We argue that the fermionic zero mode in non-trivial gauge field backgrounds must have a zero. We demonstrate this explicitly for calorons where its location is related to a constituent monopole. Furthermore a topological reasoning for the existence of the zero is given which therefore will be present for any non-trivial configuration. We propose the use of this property in particular for lattice simulations in order to uncover the topological content of a configuration.Comment: 6 pages, 3 figures in 5 part

Anderson localization through Polyakov loops: lattice evidence and Random matrix model

We investigate low-lying fermion modes in SU(2) gauge theory at temperatures above the phase transition. Both staggered and overlap spectra reveal transitions from chaotic (random matrix) to integrable (Poissonian) behavior accompanied by an increasing localization of the eigenmodes. We show that the latter are trapped by local Polyakov loop fluctuations. Islands of such "wrong" Polyakov loops can therefore be viewed as defects leading to Anderson localization in gauge theories. We find strong similarities in the spatial profile of these localized staggered and overlap eigenmodes. We discuss possible interpretations of this finding and present a sparse random matrix model that reproduces these features.Comment: 11 pages, 23 plots in 11 figures; some comments and references added, some axis labels corrected; journal versio

The State of the Art in Global Modeling

Ever since its foundation, IIASA has assumed a monitoring role in the field of Global Modeling. Whenever a major model reached a state of completion, a IIASA conference was convened in which this model was presented and discussed by a (rapidly emerging) "Global Modeling Community" of scholars actively or passively working on global models or problems of global modeling. The 6th IIASA Global Modeling Conference, held at IIASA 17-20 October 1978, was different in scope in as far as it was mainly devoted to an assessment of the state-of-the-art. The first (major) part of the conference was organized around seven major topics (rather than models); all contributions and papers pertaining to this first part have been incorporated into a book, probably to appear under the title "Groping in the Dark". The second part of the Conference was, as usually, devoted to a presentation and discussion of ongoing modeling work. It is the papers belonging to this second part which should have been assembled in a separate volume. It deserves to be emphasized that these papers should not merely be considered an appendix to "Groping in the Dark"; from what was said above, it should be clear that the second part of the Conference was sufficiently independent from the first part to warrant a publication per se. As the 7th IIASA Global Modeling Conference was devoted to a special problem (environmental aspects in global models) and the 8th Conference will again be devoted to a special problem (international economic modeling), these papers represent a rather comprehensive overview of all major methodological and practical work recently done in global modeling or, in other words, the latest somewhat complete assembly of reports on global modeling work available for sometime to come. Unfortunately, for technical reasons it has been impossible to publish these papers -- covering some 800 pages -- in traditional form. IIASA must limit itself to making all papers not published elsewhere available to an interested scientific community in the form of microfiche. This Collaborative Paper, therefore, gives only a list of these papers, plus background information about the Conference. Microfiche copies of the individual papers are available on request from the IIASA Publications Department, A-2361 Laxenburg, Austria (www.iiasa.ac.at/Publications; [email protected])

Local CP-violation and electric charge separation by magnetic fields from lattice QCD

We study local CP-violation on the lattice by measuring the local correlation between the topological charge density and the electric dipole moment of quarks, induced by a constant external magnetic field. This correlator is found to increase linearly with the external field, with the coefficient of proportionality depending only weakly on temperature. Results are obtained on lattices with various spacings, and are extrapolated to the continuum limit after the renormalization of the observables is carried out. This renormalization utilizes the gradient flow for the quark and gluon fields. Our findings suggest that the strength of local CP-violation in QCD with physical quark masses is about an order of magnitude smaller than a model prediction based on nearly massless quarks in domains of constant gluon backgrounds with topological charge. We also show numerical evidence that the observed local CP-violation correlates with spatially extended electric dipole structures in the QCD vacuum.Comment: 19 pages, 7 figures. Additional lattice results about the induced electric dipole structure, extended model description, specified terminology. Version published in JHE

Probing for Instanton Quarks with epsilon-Cooling

We use epsilon-cooling, adjusting at will the order a^2 corrections to the lattice action, to study the parameter space of instantons in the background of non-trivial holonomy and to determine the presence and nature of constituents with fractional topological charge at finite and zero temperature for SU(2). As an additional tool, zero temperature configurations were generated from those at finite temperature with well-separated constituents. This is achieved by "adiabatically" adjusting the anisotropic coupling used to implement finite temperature on a symmetric lattice. The action and topological charge density, as well as the Polyakov loop and chiral zero-modes are used to analyse these configurations. We also show how cooling histories themselves can reveal the presence of constituents with fractional topological charge. We comment on the interpretation of recent fermion zero-mode studies for thermalized ensembles at small temperatures.Comment: 26 pages, 14 figures in 33 part

Chiral condensate and dressed Polyakov loop in the Nambu--Jona-Lasinio model

We investigate the chiral condensate and the dressed Polyakov loop or dual chiral condensate at finite temperature and density in two-flavor Nambu--Jona-Lasinio model. The dressed Polyakov loop is regarded as an equivalent order parameter of deconfinement phase transition in a confining theory. We find the behavior of dressed Polyakov loop in absence of any confinement mechanism is quite interesting, with only quark degrees of freedom present, it still shows an order parameter like behavior. It is found that in the chiral limit, the critical temperature for chiral phase transition coincides with that of the dressed Polyakov loop in the whole $(T,\mu)$ plane. In the case of explicit chiral symmetry breaking, it is found that the transition temperature for chiral restoration $T_c^{\chi}$ is smaller than that of the dressed Polyakov loop $T_c^{{\cal D}}$ in the low baryon density region where the transition is a crossover. With the increase of current quark mass the difference between the two transition temperatures is found to be increasing. However, the two critical temperatures coincide in the high baryon density region where the phase transition is of first order. We give an explanation on the feature of $T_c^{\chi}=T_c^{\cal D}$ in the case of 1st and 2nd order phase transitions, and $T_c^{\chi}<T_c^{\cal D}$ in the case of crossover, and expect this feature is general and can be extended to full QCD theory. Our result might indicate that in the case of crossover, there exists a small region where chiral symmetry is restored but the color degrees of freedom are still confined.Comment: 7 pages, 10 figure

Environmental Aspects in Global Modeling. Proceedings of the 7th IIASA Symposium on Global Modeling

The Seventh Global Modeling Conference concentrated on a key problem that, it was felt, deserved special attention, namely, the role of the environment in global modeling. The purpose of the conference was not so much to look back on what had been achieved (or remained to be done), but rather to examine what should be learnt for future modeling work from past achievements or omissions. It is hoped that the papers presented in this volume will give an overview of the problematique and of possibilities for future advances

Input-Output Approaches in Global Modeling; Proceedings of the Fifth IIASA Symposium on Global Modeling, September 26-29, 1977

Since 1974, the International Institute for Applied Systems Analysis has been monitoring developments in the field of global modeling. The IIASA conferences on global modeling are intended to serve as a forum for exchanging information among modeling groups. This conference focused on a methodology; the models discussed were all constructed with input-output techniques. The main part of the conference was devoted to the Leontief model, "The Future of the World Economy," and FUGI, Future of Global Interdependence, a model developed by a group of Japanese scientists. FUGI includes a global input-output model, a global macroeconomic model, and a global metallic resources model, and is published here in full for the first time in English. Reports on other input-output models include a survey of work in the USSR, as well as examples of work in progress in the FRG, the United Kingdom, Poland, and the United States

Latin American World Model. Proceedings of the Second IIASA Symposium on Global Modelling

The mathematical model presented here is normative; the concern is not with predicting what will occur if the contemporary tendencies of mankind continue, but rather with sketching a way of arriving at the final goal of a world liberated from backwardness and misery. Any long-term forecast about the development of mankind is based on a view of the world rooted in a particular value system. By assuming that the structure of the contemporary world and the set of values which sustains it may be linearly projected toward the future, we are in fact taking a position. In this sense, the difference which is usually made between a projective and normative model is essentially fallacious. The idea of constructing this model springs from a meeting held in 1970 in Rio de Janeiro sponsored jointly by the Club of Rome and the Instituto Universitario de Pesquisas do Rio de Janeiro. The meeting analyzed and discussed the results of the World Model 111 which was constructed by the group headed by Meadows at the Sloan School of Management of the Massachusetts Institute of Technology (MIT). As a result of the discusion of the basic assumptions of the World Model III, a group of Latin Americans attending the meeting decided to assign the Fundacion Bariloche of Argentina the work of constructing a world model that encorporated the views expressed at the meeting. A Committee was formed composed of Helio Jaguaribe, Carlos A. Mallmann, Enrique Oteiza, Jorge Sabato, Osvaldo Sunkel, Victor Urquidi, and Amilcar Herrera, which in September 1971 issued a paper giving in general terms the fundamental hypotheses and variables to be used in the Bariloche Model. This preliminary project was submitted to the annual meeting of the Consejo Latinoamericano de Ciencias Sociales (CLACSO), held in Buenos Aires in December 1971. In mid-1971, a meeting was held at the Fundacion Bariloche, attended by the majority of the members of the Committee as well as by some of those who would later be involved as authors in the project. The meeting defined the essential features of the Model to be developed. The Committee appointed a Project Director, and entrusted him with the task of forming the group of specialists who would construct the model. In the final phase of the project Hugo Scolnik was appointed Co-Director of the project. While an individual author has reported on the main task assigned him, this in no way reflects the real participation that each had in the work. The hypotheses and basic philosophy of the model were the product of a long and difficult collective task, and it is almost impossible to distinguish the individual contributions. The initial group which gave rise to the project constituted itself thereafter into a Consulting Committee, with the mission of periodically carrying out a critical analysis of the progress of the work. Its criticisms and suggestions were a valuable contribution to the task performed. It is appropriate to point out that final responsibility for the ideas contained in the model is with the authors. An initial contribution was received from the Club of Rome to carry out a study on the project's feasibility. Thereafter, the execution of the project was financed in full by the International Development Research Centre (IDRC), Ottawa, Canada. The authors wish to express their gratitude to both institutions for the total academic freedom given them