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Mini-workshop on New Developments in Lattice Gauge Theory
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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
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Program
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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)
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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
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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.
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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.
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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.
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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.
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4th April 2000