Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2000-02-09
Nucl.Phys. B585 (2000) 471-513
Physics
High Energy Physics
High Energy Physics - Lattice
uses phyzzx.tex and phyzzx.plus, 57 pages, the final version to appear in Nucl. Phys. B
Scientific paper
10.1016/S0550-3213(00)00408-9
We study the gauge anomaly ${\cal A}$ defined on a 4-dimensional infinite lattice while keeping the lattice spacing finite. We assume that (I) ${\cal A}$ depends smoothly and locally on the gauge potential, (II) ${\cal A}$ reproduces the gauge anomaly in the continuum theory in the classical continuum limit, and (III) U(1) gauge anomalies have a topological property. It is then shown that the gauge anomaly ${\cal A}$ can always be removed by local counterterms to all orders in powers of the gauge potential, leaving possible breakings proportional to the anomaly in the continuum theory. This follows from an analysis of nontrivial local solutions to the Wess-Zumino consistency condition in lattice gauge theory. Our result is applicable to the lattice chiral gauge theory based on the Ginsparg-Wilson Dirac operator, when the gauge field is sufficiently weak $\|U(n,\mu)-1\|<\epsilon'$, where $U(n,\mu)$ is the link variable and $\epsilon'$ a certain small positive constant.
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