Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2002-10-11
JHEP 0301 (2003) 075
Physics
High Energy Physics
High Energy Physics - Lattice
31 pages. LaTeX, feynmf. Minor changes, references added and typos corrected. Final version published in JHEP
Scientific paper
10.1088/1126-6708/2003/01/075
We formulate lattice perturbation theory for gauge theories in noncommutative geometry. We apply it to three-dimensional noncommutative QED and calculate the effective action induced by Dirac fermions. In particular "parity invariance" of a massless theory receives an anomaly expressed by the noncommutative Chern-Simons action. The coefficient of the anomaly is labelled by an integer depending on the lattice action, which is a noncommutative counterpart of the phenomenon known in the commutative theory. The parity anomaly can also be obtained using Ginsparg-Wilson fermions, where the masslessness is guaranteed at finite lattice spacing. This suggests a natural definition of the lattice-regularized Chern-Simons theory on a noncommutative torus, which could enable nonperturbative studies of quantum Hall systems.
Nishimura Jun
Vazquez-Mozo Miguel Angel
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