Anomaly In Lattice Gauge Theory Research Articles

Non-commutative differential calculus and the axial anomaly in Abelian lattice gauge theories

The axial anomaly in lattice gauge theories has a topological nature when the Dirac operator satisfies the Ginsparg–Wilson relation. We study the axial anomaly in Abelian gauge theories on an infinite hypercubic lattice by utilizing cohomological arguments. The crucial tool in our approach is the non-commutative differential calculus (NCDC) which makes the Leibniz rule of exterior derivatives valid on the lattice. The topological nature of the “Chern character” on the lattice becomes manifest in the context of NCDC. Our result provides an algebraic proof of Lüscher's theorem for a four-dimensional lattice and its generalization to arbitrary dimensions.

Mathematical derivation of chiral anomaly in lattice gauge theory with Wilson’s action

Chiral U(1) anomaly is derived with mathematical rigor for a Euclidean fermion coupled to a smooth external U(1) gauge field on an even dimensional torus as a continuum limit of lattice regularized fermion field theory with the Wilson term in the action. The present work rigorously proves for the first time that the Wilson term correctly reproduces the chiral anomaly.

Supercurrent anomaly in lattice gauge theory

The supercurrent and superconformal anomalies are investigated in N=1 super Yang-Mills theory using the lattice regularization. It is shown that for a wide class of the choice for the action and the supercurrent, the anomaly structure is the same as that in the continuum theory.