Propagators in Noncommutative Instantons

TL;DR

This paper constructs explicit Green functions for fields in noncommutative instanton backgrounds, revealing how noncommutativity affects propagators differently depending on the gauge representation.

Contribution

It provides explicit formulas for propagators in noncommutative instanton backgrounds, highlighting differences between adjoint and fundamental representations.

Findings

Adjoint representation propagators are deformed by noncommutativity.

Fundamental representation propagators remain unchanged from the commutative case.

Explicit construction of Green functions for various fields in noncommutative instantons.

Abstract

We explicitly construct Green functions for a field in an arbitrary representation of gauge group propagating in noncommutative instanton backgrounds based on the ADHM construction. The propagators for spinor and vector fields can be constructed in terms of those for the scalar field in 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 the commutative case.