Mini-workshop: New Developments in Lattice Gauge Theory

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.

Schedule

Abstracts

Fujikawa:

• 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.

• Index Theorem and Anomaly on the Lattice

Chiu:

• 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.

• 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:

• 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.

• 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.

Participant information

Venue

The Special Research Centre for the Subatomic Structure of Matter (CSSM) at the University of Adelaide is located at:
Level 4, 10 Pulteney St. Adelaide 5005, Australia

Registration

All are welcome. There is no registration fee.

Organisers

Sponsored by

• The Centre for the Subatomic Structure of Matter (CSSM)
• Institute for Geometry and its Applications (IGA)