Anomaly Cancellation Condition in Lattice Gauge Theory

We show that, to all orders of powers of the gauge potential, a gauge anomaly A defined on 4-dimensional infinite lattice can always be removed by a local counterterm, provided that A depends smoothly and locally on the gauge potential and that A reproduces the gauge anomaly in the continuum theory in the classical continuum limit: The unique exception is 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, μ)−1‖ < ǫ, where U(n, μ) is the link variable and ǫ a certain small positive constant. PACS numbers: 11.15.Ha, 11.30.Rd