Scale-dependent Planck mass and Higgs VEV from holography and functional renormalization

TL;DR

This paper investigates how the Planck mass and Higgs vacuum expectation value change with scale using holographic and functional renormalization methods, indicating a possible ultraviolet fixed point in the coupled theory.

Contribution

It compares holographic and functional renormalization approaches to study scale dependence of fundamental parameters, revealing consistent results and insights into the theory's ultraviolet behavior.

Findings

Both methods yield similar scale-dependent results.

Evidence suggests the theory approaches a non-trivial ultraviolet fixed point.

Holographic and functional methods are complementary in this analysis.

Abstract

We compute the scale-dependence of the Planck mass and of the vacuum expectation value of the Higgs field using two very different renormalization group methods: a "holographic" procedure based on Einstein's equations in five dimensions with matter confined to a 3-brane, and a "functional" procedure in four dimensions based on a Wilsonian momentum cutoff. Both calculations lead to very similar results, suggesting that the coupled theory approaches a non-trivial fixed point in the ultraviolet.