Classical running and symmetry breaking in models with two extra dimensions

TL;DR

This paper studies a six-dimensional scalar model with brane-localized potential, revealing classical running of couplings, symmetry breaking, and a light state near a critical coupling, with implications for extra-dimensional theories.

Contribution

It introduces a classical renormalization group analysis of brane-localized potentials in six dimensions, showing symmetry breaking and massless modes at a specific bare coupling.

Findings

Classical running of couplings due to brane regularization.

Existence of a critical coupling where the zero mode is massless.

Spontaneous symmetry breaking above the critical coupling.

Abstract

We consider a codimension two scalar theory with brane-localised Higgs type potential. The six-dimensional field has Dirichlet boundary condition on the bounds of the transverse compact space. The regularisation of the brane singularity yields renormalisation group evolution for the localised couplings at the classical level. In particular, a tachyonic mass term grows at large distances and hits a Landau pole. We exhibit a peculiar value of the bare coupling such that the running mass parameter becomes large precisely at the compactification scale, and the effective four-dimensional zero mode is massless. Above the critical coupling, spontaneous symmetry breaking occurs and there is a very light state.