star-Cohomology, Connes-Chern Characters, and Anomalies in General Translation-Invariant Noncommutative Yang-Mills

TL;DR

This paper explores the topological aspects of translation-invariant noncommutative Yang-Mills theories using star-cohomology, linking it to cyclic cohomology and the Seiberg-Witten map to deepen understanding of anomalies.

Contribution

It introduces star-cohomology as a new framework bridging de Rham and cyclic cohomology for noncommutative gauge theories, providing a cohomological formulation of anomalies.

Findings

Star-cohomology effectively characterizes topological structures in noncommutative Yang-Mills theories.

The framework connects to Connes-Chern characters and anomalies in noncommutative geometry.

Provides a cohomological perspective similar to the Seiberg-Witten map.

Abstract

Topological structure of translation-invariant noncommutative Yang-Mills theories are studied by means of a cohomology theory, so called star-cohomology, which plays an intermediate role between de Rham and cyclic (co)homology theory for noncommutative algebras and gives rise to a cohomological formulation comparable to Seiberg-Witten map.