Gravitational Corrections to $\Phi^{4}$ Theory with Spontaneously Broken Symmetry

TL;DR

This paper investigates how quantum gravitational effects influence the renormalization of a complex scalar field with spontaneous symmetry breaking, finding that gravity-induced corrections cause inconsistencies in the Higgs sector's renormalization.

Contribution

It provides the first analysis of gravitational corrections to the Higgs sector in a spontaneously broken scalar theory within an effective quantum gravity framework.

Findings

Gravitational corrections destabilize Higgs sector renormalization.

Pure scalar corrections are compatible with standard renormalization.

Gravity effects become significant near the Planck scale.

Abstract

We consider a complex scalar $\Phi^4 $ theory with spontaneously broken global U(1) symmetry, minimally coupling to perturbatively quantized Einstein gravity which is treated as an effective theory at the energy well below the Planck scale. Both the lowest order pure real scalar correction and the gravitational correction to the renormalization of the Higgs sector in this model have been investigated. Our results show that the gravitational correction renders the renormalization of the Higgs sector in this model inconsistent while the pure real scalar correction to it leads to a compatible renormalization.