More about the axial anomaly on the lattice
arXiv:hep-lat/0206003 · doi:10.1016/S0550-3213(02)00812-X
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.
12 pages, uses JHEP.cls and amsfonts.sty, the final version to appear in Nucl. Phys. B
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Cited by in corpus (11)
- Axial anomaly with the overlap-Dirac operator in arbitrary dimensions
- Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice
- Chiral anomalies in the reduced model
- A simple construction of fermion measure term in U(1) chiral lattice gauge theories with exact gauge invariance
- A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance
- A numerical solution to the local cohomology problem in U(1) chiral gauge theories
- Anomalous gauge theories revisited
- Axial anomaly in the reduced model: Higher representations
- Wess-Zumino-Witten term on the lattice
- Spectrum of the Hermitian Wilson-Dirac Operator for a Uniform Magnetic Field in Two Dimensions
- Axial anomaly in the reduced model: Higher representations