Approximate Lorentz invariance of the vacuum: a physical solution of the `hierarchy problem' ?

TL;DR

The paper proposes that approximate Lorentz invariance in the vacuum, linked to the Higgs condensate, could offer a physical explanation for the hierarchy problem by connecting infrared and ultraviolet scales.

Contribution

It introduces a novel perspective that the hierarchy problem can be addressed through the infrared-ultraviolet connection in the Higgs condensate, challenging traditional views.

Findings

Relation between 'delta', 'Lambda', and the Fermi scale suggests a solution to the hierarchy problem.

Vacuum Lorentz invariance is approximate, not exact, at ultralow momenta.

The Planck scale encodes an infrared-ultraviolet connection in the scalar condensate.

Abstract

In the `condensed phase' of effective quantum field theories one expects deviations from exact Lorentz invariance at ultralow momenta | k| < delta where the shell 'delta' should only vanish in the strict local limit of the theory when the ultraviolet cutoff 'Lambda' tends to infinity. I explore this idea for the Higgs condensate suggesting that, in this case, the resulting relation connecting 'delta', 'Lambda' and the Fermi scale might provide a simple physical solution of the `hierarchy problem'. In this picture, the Planck scale is not a purely ultraviolet quantity but embodies in its numerical value the peculiar infrared-ultraviolet connection that is realized in the scalar condensate.