............................................................................... Mini-workshop on New Developments in Lattice Gauge Theory ............................................................................... Jointly sponsored by The Centre for the Subatomic The Institute for Geometry and Structure of Matter (CSSM) its Applications (IGA) Place: CSSM, Adelaide Date: 4-5 April, 2000 Invited speakers: Prof. Kazuo Fujikawa (University of Tokyo) Prof. Ting-Wai Chiu (National Taiwan University) Dr. Urs Heller (CSIT, Florida State University) The mini-workshop will focus on new developments in lattice gauge theory involving lattice Dirac operators satisfying the Ginsparg--Wilson relation. These provide a way around traditional problems associated with fermions on the lattice, and are moreover able to capture topological features of the continuum theory associated with anomalies and the Index Theorem. Topics will include: exact chiral symmetry, anomalies, topological aspects and lattice Index Theory, chiral symmetry breaking and topology in QCD with Overlap-Dirac operator. A number of the talks will be expository and are intended to provide an introduction to these developments. All are welcome. There is no registration fee. Further information can be obtained from: David Adams Tony Williams dadams@maths.adelaide.edu.au awilliam@physics.adelaide.edu.au See also the CSSM and IGA webpages: http://www.physics.adelaide.edu.au/cssm/workshops/Mini_Latt_00.html http://www.maths.adelaide.edu.au/iga/lgt ......................... Program ......................... Tuesday 4 April: Wednesday 5 April: 9.30 Fujikawa 2 10.30 Coffee 10.30 discussion 10.50 Opening 10.45 coffee 11.00 Fujikawa 1 11.15 Adams 12.00 discussion 12.15 discussion 12.15 lunch 12.30 lunch 14.00 Chiu 1 14.00 Chiu 2 15.00 discussion 15.00 discussion 15.15 coffee 15.15 coffee 15.45 Heller 1 15.45 Heller 2 16.45 discussion 16.45 discussion 17.00 Wine reception 17.00 end at the CSSM Evening Dinner (details TBA) ......................................................................... Titles and abstracts of the talks: Fujikawa: 1. History and Formulation of Anomalies This talk is intended to those people who are interested in some basic aspects of anomalies or have no previous research experiences in anomalies. 2. Index Theorem and Anomaly on the Lattice ------------------------------- Chiu: 1. Chiral Fermions on a Finite Lattice We discuss how to formulate Dirac fermion operator on a finite lattice such that it can provide a nonperturbative regularization for massless fermions interacting with a background gauge field. The basic properties of lattice Dirac operator satisfying the Ginsparg-Wilson relation are reviewed. 2. Topological Characteristics of Lattice Dirac Operators We show that even if a lattice Dirac operator satisfies the conditions consisting of locality, free of species doublings, correct continuum behavior, gamma5-hermiticity and the Ginsparg-Wilson relation, it does not necessarily have exact zero modes in nontrivial gauge backgrounds. This implies that each lattice Dirac operator has its own topological characteristics which cannot be fixed by these conditions. The role of topological characteristics in the axial anomaly is derived explicitly. ------------------------------- Heller: 1. Overlap Fermions for QCD: Topology and Chiral Symmetry Breaking A short introduction to the overlap formalism for chiral fermions is presented. The overlap Dirac operator is derived and its relation to the effective Dirac operator of domain wall fermions is given. Properties of overlap fermions are explained, in particular the existence of exact zero modes in topologically non-trivial gauge fields. The results of a study of chiral symmetry breaking in QCD with overlap fermions are presented, and finally some preliminary spectroscopy results are shown. 2. Numerical Techniques for Overlap Fermions Overlap fermions, and their relation to domain wall fermions, are briefly reviewed. The overlap Dirac operator contains the sign function of a large, but sparse, hermitian operator. Techniques for dealing with this sign function numerically are presented. The challenges for simulations on presently accessible lattices are illustrated both for overlap and domain wall fermions. Some avenues for possible improvement of the numerical techniques are discussed. -------------------------------- Adams: Aspects of Chiral Gauge Theory and Index Theory on the Lattice In the continuum there is an intimate relation between global obstructions to gauge-invariance of the fermionic determinant in chiral gauge theory and results in Index Theory. I will describe how these global obstructions, and their index-theoretic interpretations, are reproduced in the Overlap formulation of chiral gauge theory on the lattice. ......................................................................... About the invited speakers: Prof. Fujikawa is an eminent theoretical physicist best known for discovering the nonperturbative nature of anomalies in QFT and their connection with the Atiyah--Singer Index Theorem. His recent work includes an investigation of the axial anomaly for the new lattice Dirac operators, clarifying its relation to the continuum anomaly. Prof. Chiu and Dr. Heller have made important contributions to the new developments in lattice gauge theory. Prof. Chiu's work has focussed on understanding the structure of solutions to the Ginsparg--Wilson relation and investigating their topological properties. Dr. Heller and his collaborators have developed techniques for numerically implementing the Overlap-Dirac operator (the main solution to the GW relation) and used this to study chiral symmetry breaking and topology in QCD. ......................................................................... 4th April 2000