UV/IR Mixing for Noncommutative Complex Scalar Field Theory, II (Interaction with Gauge Fields)

TL;DR

This paper investigates the one-loop renormalizability and infrared singularities in noncommutative scalar electrodynamics and N=2 SUSY Yang-Mills theory, revealing conditions for renormalizability and the role of fermions in IR behavior.

Contribution

It demonstrates the specific form of the scalar potential needed for renormalizability and shows how fermion contributions restore expected potential forms, ensuring IR finiteness in noncommutative SUSY gauge theories.

Findings

Scalar potential must be an anticommutator squared for renormalizability.

Fermion contributions restore the commutator in the scalar potential.

IR singularities are absent in noncommutative N=2 SUSY gauge theory.

Abstract

We consider noncommutative analogs of scalar electrodynamics and N=2 D=4 SUSY Yang-Mills theory. We show that one-loop renormalizability of noncommutative scalar electrodynamics requires the scalar potential to be an anticommutator squared. This form of the scalar potential differs from the one expected from the point of view of noncommutative gauge theories with extended SUSY containing a square of commutator. We show that fermion contributions restore the commutator in the scalar potential. This provides one-loop renormalizability of noncommutative N=2 SUSY gauge theory. We demonstrate a presence of non-integrable IR singularities in noncommutative scalar electrodynamics for general coupling constants. We find that for a special ratio of coupling constants these IR singularities vanish. Also we show that IR poles are absent in noncommutative N=2 SUSY gauge theory.