New Developments in Quantum Field Theory

Transcription

1 New Developments in Quantum Field Theory

2 NATO ASI Series Advanced Science Institutes Series A series presenting the results of activities sponsored by the NATO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities. The series is published by an international board of publishers in conjunction with the NATO Scientific Affairs Division A Life Sciences Plenum Publishing Corporation B Physics New York and London C Mathematical Kluwer Academic Publishers and Physical Sciences Dordrecht, Boston, and London D Behavioral and Social Sciences E Applied Sciences F Computer and Systems Sciences Springer-Verlag G Ecological Sciences Berlin, Heidelberg, New York, London, H Cell Biology Paris, Tokyo, Hong Kong, and Barcelona I Global Environmental Change PARTNERSHIP SUB-SERIES 1. Disarmament Technologies 2. Environment 3. High Technology 4. Science and Technology Policy 5. Computer Networking Kluwer Academic Publishers Springer-Verlag Kluwer Academic Publishers Kluwer Academic Publishers Kluwer Academic Publishers The Partnership Sub-Series incorporates activities undertaken in collaboration with NATO s Cooperation Partners, the countries of the CIS and Central and Eastern Europe, in Priority Areas of concern to those countries. Recent Volumes in this Series: Volume 364 Quantum Fields and Quantum Space Time edited by Gerard 't Hooft, Arthur Jaffe, Gerhard Mack, Pronob K. Mitter, and Raymond Stora Volume 365 Techniques and Concepts of High-Energy Physics IX edited by Thomas Ferbel Volume 366 New Developments in Quantum Field Theory edited by Poul Henrik Damgaard and Jerzy Jurkiewicz Series B: Physics

3 New Developments in Quantum Field Theory Edited by Poul Henrik Damgaard Niels Bohr Institute Copenhagen, Denmark and Jerzy Jurkiewicz Jagellonian University Cracow, Poland KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW

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5 PREFACE Quantum field theory is one of most central constructions in 20th century theoretical physics, and it continues to develop rapidly in many different directions. The aim of the workshop New Developments in Quantum Field Theory, which was held in Zakopane, Poland, June 14-20, 1997, was to capture a broad selection of the most recent advances in this field. The conference was sponsored by the Scientific and Environmental Affairs Division of NATO, as part of the Advanced Research Workshop series. This book contains the proceedings of that meeting. Major topics covered at the workshop include quantized theories of gravity, string theory, conformal field theory, cosmology, field theory approaches to critical phenomena and the renormalization group, matrix models, and field theory techniques applied to the theory of turbulence. One common theme at the conference was the use of large-n matrix models to obtain exact results in a variety of different disciplines. For example, it has been known for several years that by taking a suitable double-scaling limit, certain string theories (or two-dimensional quantum gravity coupled to matter) can be re-obtained from the large-n expansion of matrix models. There continues to be a large activity in this area of research, which was well reflected by talks given at our workshop. Remarkably, large- N matrix models have very recently just a few months before our meeting been shown to have yet another deep relation to string theory. This time the connection goes through the so-called M-theory, which can loosely be thought of as a unifying theory of strings. Also this very recent subject was covered at our workshop. At the very last moment Yuri Makeenko had to cancel his participation. He fortunately agreed to send his contribution to this volume. The understanding of the rôle M-theory plays for the different string theories originates in some remarkable results concerning duality that have been uncovered within the last 2-3 years. While so-called T-duality of string theory has been known for years, it is now being seen in a new light, and also other kinds of dualities have been found. Simultaneously, exact or approximate dualities have been shown to be properties of certain highly non-trivial supersymmetric quantum field theories in four dimensions. Both these dualities, their origin in string theory, as well as direct analyses of T-duality in the σ-model language were discussed at the meeting. Another recent application of large-n matrix model techniques has been in the description of certain exact features of field theories with spontaneous chiral symmetry breaking (such as Quantum Chromodynamics). A recent flurry of activity has revealed a number of surprising universal aspects of such quantum field theories, related to the spectrum of the Dirac operator. At the meeting new and impressive Monte Carlo results from lattice gauge theory simulations were presented. They appeared to be in complete v

6 agreement with the theoretical predictions. Also other aspects of this computational framework of matrix models were discussed at the meeting, for example in connection with the behavior at finite temperature, or in the limiting case of no chiral symmetry breaking. One final, and also surprising, application of large-n matrix models which was covered at the workshop concerns the derivation of exact results in the theory of turbulence. Enlightening lectures were also given on the use of quantum field theory techniques in general to solve problems related to turbulence, and on the application of magnetohydrodynamics on cosmological scales. As testified by this volume, numerous other topics were discussed at our workshop. It left the participants with the distinct impression that despite the long history of the field, we are now witnessing an extremely fruitful period of developments in quantum field theory. We take this opportunity to thank Yu. Makeenko, A. Polychronakos and J.F. Wheater for serving on the international advisory committee. Very special thanks go to M. Praszalowicz and B. Brzezicka for their tireless help both before and during the workshop, and to P. Bialas, Z. Burda, and P. Jochym for much assistance. We would in particular like to thank Z. Burda for his help in preparing this volume. Copenhagen and Cracow Poul H. Damgaard Jerzy Jurkiewicz vi

7 CONTENTS LECTURERS The Structure of 2D Quantum Space-Time J. Ambjørn Scaling Laws in Turbulence K. Gaw dzki Field Theory as Free Fall A. Carlini and J. Greensite Center Dominance, Center Vortices, and Confinement L. Del Debbio, M. Faber, J. Greensite and Š. Olejník Duality and the Renormalization Group P.E. Haagensen Unification of the General Non-Linear Sigma Model and the Virasoro Master Equation J. de Boer and M. Halpern A Matrix Model Solution of the Hirota Equation V.A. Kazakov Lattice Approximation of Quantum Electrodynamics J. Kijowski and Gerd Rudolph Three Introductory Talks on Matrix Models of Superstrings Y. Makeenko New Developments in the Continuous Renormalization Group T.R. Morris vii

8 Primordial Magnetic Fields and Their Development (Applied Field Theory) P. Olesen Towards Matrix Models of IIB Superstrings P. Olesen Quantum Mechanics of the Electric Charge A. Staruszkiewicz Universal Fluctuations in Dirac Spectra J. Verbaarschot Determination of Critical Exponents and Equation of State by Field Theory Methods J. Zinn-Justin SEMINAR SPEAKERS Collective Dynamics of a Domain Wall H. Arod Path Space Formulation of the BFV Theorem K. Bering Surplus Anomaly and Random Geometries P. Bialas, Z. Burda and D. Johnston Topological Contents of 3D Seiberg-Witten Theory B. Broda Free Strings in Non-Critical Dimensions M. Daszkiewicz, Z. Hasiewicz and Z. Jaskólski Seiberg-Witten Theory, Integrable Systems and D-Branes A. Marshakov Microscopic Universality in Random Matrix Models of QCD S.M. Nishigaki New Developments in Non-Hermitian Random Matrix Models R.A. Janik, M.A. Nowak, G. Papp and I. Zahed Potential Topography and Mass Generation M. Kudinov, E. Moreno and P. Orland viii

9 Past the Highest-Weight, and What You Can Find There A.M. Semikhatov The Spectral Dimension on Branched Polymer Ensembles T. Jonsson and J.F. Wheater Solving the Baxter Equation in High Energy QCD J. Wosiek Participants Index ix