A Noncommutative Deformation of Topological Field Theory

Abstract

Cohomological Yang-Mills theory is formulated on a noncommutative differentiable four manifold through the $\theta$-deformation of its corresponding BRST algebra. The resulting noncommutative field theory is a natural setting to define the $\theta$-deformation of Donaldson invariants and they are interpreted as a mapping between the Chevalley-Eilenberg homology of noncommutative spacetime and the Chevalley-Eilenberg cohomology of noncommutative moduli of instantons. In the process we find that in the weak coupling limit the quantum theory is localized at the moduli space of noncommutative instantons.

arXiv comment11+1 pages, revtex4, no figures

References in corpus (9)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Instantons on noncommutative R^4, and (2,0) superconformal six dimensional theory
• The Standard Model on Non-Commutative Space-Time
• Noncommutative Instantons and Twistor Transform
• Noncommutative Self-dual Gravity
• Noncommutative Topological Theories of Gravity
• BRST Quantization of Noncommutative Gauge Theories
• Noncommutative Cohomological Field Theory and GMS soliton

Cited by in corpus (2)

• Instantons, Fluxons and Open Gauge String Theory
• One-loop Renormalized Coefficient of Noncommutative Supersymmetric Yang-Mills-Chern-Simons Gauge Theories in Three Dimensions