Chiral Anomaly and Ginsparg-Wilson Relation on the Noncommutative Torus
Satoshi Iso, Keiichi Nagao
TL;DR
This paper investigates the chiral anomaly on the noncommutative torus using the overlap Dirac operator and Ginsparg-Wilson relation, revealing its topological nature related to the Chern character with star products.
Contribution
It demonstrates the form of the chiral anomaly on the noncommutative torus as a Chern character, extending the understanding of anomalies in noncommutative geometry.
Findings
Chiral anomaly expressed as a Chern character with star products.
Utilizes Ginsparg-Wilson relation in arbitrary even dimensions.
Provides a topological argument for anomaly structure.
Abstract
We evaluate chiral anomaly on the noncommutative torus with the overlap Dirac operator satisfying the Ginsparg-Wilson relation in arbitrary even dimensions. Utilizing a topological argument we show that the chiral anomaly is combined into a form of the Chern character with star products.
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