We explicitly construct Green’s functions for a field in an arbitrary representation of a gauge group propagating in noncommutative instanton backgrounds based on the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction. The propagators for spinor and vector fields can be constructed in terms of those for the scalar field in a noncommutative instanton background. We show that the propagators in the adjoint representation are deformed by noncommutativity while those in the fundamental representation have exactly the same form as in the commutative case.

• Received 11 June 2002

DOI:https://doi.org/10.1103/PhysRevD.66.045027