More about the axial anomaly on the lattice
Abstract
We study the axial anomaly defined on a finite-size lattice by using a Dirac operator which obeys the Ginsparg-Wilson relation. When the gauge group is U(1), we show that the basic structure of axial anomaly on the infinite lattice, which can be deduced by a cohomological analysis, persists even on (sufficiently large) finite-size lattices. For non-abelian gauge groups, we propose a conjecture on a possible form of axial anomaly on the infinite lattice, which holds to all orders in perturbation theory. With this conjecture, we show that a structure of the axial anomaly on finite-size lattices is again basically identical to that on the infinite lattice. Our analysis with the Ginsparg-Wilson Dirac operator indicates that, in appropriate frameworks, the basic structure of axial anomaly is quite robust and it persists even in a system with finite ultraviolet and infrared cutoffs.
Keywords
Cite
@article{arxiv.hep-lat/0206003,
title = {More about the axial anomaly on the lattice},
author = {Hiroshi Igarashi and Kiyoshi Okuyama and Hiroshi Suzuki},
journal= {arXiv preprint arXiv:hep-lat/0206003},
year = {2010}
}
Comments
12 pages, uses JHEP.cls and amsfonts.sty, the final version to appear in Nucl. Phys. B