Effective Potential and Spontaneous Symmetry Breaking in the Noncommutative phi^6 Model

TL;DR

This paper analyzes how noncommutative effects in a phi^6 model can induce spontaneous symmetry breaking through modifications of the effective potential, especially in the nonplanar sector at the two-loop level.

Contribution

It demonstrates that noncommutative effects can significantly alter the effective potential, leading to symmetry breaking in regimes where the commutative model does not.

Findings

Noncommutative effects drastically change the effective potential shape.

Nonplanar sector can dominate and induce symmetry breaking.

Symmetry breaking occurs for parameter values beyond the commutative case.

Abstract

We study the conditions for spontaneous symmetry breaking of the (2+1)-dimensional noncommutative phi^6 model in the small-theta limit. In this regime, considering the model as a cutoff theory, it is reasonable to assume translational invariance as a property of the vacuum state and study the conditions for spontaneous symmetry breaking by an effective potential analysis. An investigation of up to the two loop level reveals that noncommutative effects can modify drastically the shape of the effective potential. Under reasonable conditions, the nonplanar sector of the theory can become dominant and induce symmetry breaking for values of the mass and coupling constants not reached by the commutative counterpart.