Two-loop effective potential in noncommutative scalar field theory

TL;DR

This paper investigates the two-loop effective potential in noncommutative scalar field theory, revealing how nonplanar diagrams influence symmetry breaking and restoration depending on the noncommutativity scale.

Contribution

It provides a detailed two-loop analysis of the effective potential, highlighting the role of nonplanar diagrams in symmetry behavior in noncommutative scalar fields.

Findings

Nonplanar diagrams are absent at one-loop but dominate at two-loop for small noncommutativity.

Radiative corrections from nonplanar diagrams can induce or restore symmetry breaking.

The study advances understanding of quantum effects in noncommutative field theories.

Abstract

The renormalization of effective potential for the noncommutative scalar field theory is investigated to the two-loop approximation. It is seen that the nonplanar diagram does not appear in the one-loop potential. However, nonplanar diagram can become dominant in the two-loop level as the noncommutativity of geometry is sufficiently small. The result shows that the radiative corrections from the nonplanar diagrams have an inclination to induce the spontaneously symmetry breaking if it is not broken in the tree level, and have an inclination to restore the symmetry breaking if it has been broken in the tree level.