Vacuum energy from noncommutative models

TL;DR

This paper investigates how noncommutative geometry models affect vacuum energy calculations, revealing that the impact on divergences varies depending on the specific model, with some reducing divergence and others not.

Contribution

The study compares different noncommutative models to determine their effects on vacuum energy divergences, highlighting that noncommutativity does not universally suppress ultraviolet divergences.

Findings

Some models show logarithmic divergence in vacuum energy.

Other models exhibit divergences stronger than in commutative theories.

The effect of noncommutativity on divergences is model-dependent.

Abstract

The vacuum energy is computed for a scalar field in a noncommutative background in several models of noncommutative geometry. One may expect that the noncommutativity introduces a natural cutoff on the ultraviolet divergences of field theory. Our calculations show however that this depends on the particular model considered: in some cases the divergences are suppressed and the vacuum energy is only logarithmically divergent, in other cases they are stronger than in the commutative theory.