More about the axial anomaly on the lattice

Details More about the axial anomaly on the lattice More about the axial anomaly on the lattice

2002-06-06

arxiv.org/abs/hep-lat/0206003v3

Nucl.Phys. B644 (2002) 383-394

Physics

High Energy Physics

High Energy Physics - Lattice

12 pages, uses JHEP.cls and amsfonts.sty, the final version to appear in Nucl. Phys. B

Scientific paper

10.1016/S0550-3213(02)00812-X

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.

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