One-loop effects in a self-dual planar noncommutative theory

TL;DR

This paper analyzes the one-loop quantum effects in a self-dual noncommutative scalar field theory in 2+1 dimensions, deriving the effective action and exploring quantum corrections around symmetry-breaking solutions.

Contribution

It provides an explicit form of the one-loop effective action for a self-dual noncommutative scalar field theory and examines quantum effects near non-trivial minima.

Findings

Explicit one-loop effective action derived.

Quantum corrections depend on classical solution amplitude.

Vacuum energy correction related to symmetry-breaking solutions.

Abstract

We study the UV properties, and derive the explicit form of the one-loop effective action, for a noncommutative complex scalar field theory in 2+1 dimensions with a Grosse-Wulkenhaar term, at the self-dual point. We also consider quantum effects around non-trivial minima of the classical action which appear when the potential allows for the spontaneous breaking of the U(1) symmetry. For those solutions, we show that the one-loop correction to the vacuum energy is a function of a special combination of the amplitude of the classical solution and the coupling constant.