Technical Naturalness on a Codimension-2 Brane

TL;DR

This paper analyzes how integrating out heavy particles on a codimension-2 brane affects brane and bulk properties, revealing potential suppression of low-energy effects in certain supersymmetric 6D models.

Contribution

It introduces a formalism for matching higher codimension branes to bulk fields and demonstrates suppression mechanisms for low-energy effective potentials.

Findings

T_2 scales as M^d, consistent with expectations.

Low-energy potential can be suppressed by factors of k^2 M^d.

Supersymmetric 6D models show similar suppression of bulk loop contributions.

Abstract

We compute how threshold effects obtained by integrating out a heavy particle localized on a codimension-2 brane influence the properties of the brane and the bulk fields it sources in D=d+2 dimensions. We do so using a recently developed formalism for matching the characteristics of higher codimension branes to the properties of the bulk fields they source. We show that although the dominant dependence on a heavy mass M that is induced in the low-energy codimension-2 tension has the generic size expected, T_2 \propto M^d, the very-low-energy effective potential governing the on-brane curvature once bulk KK modes are integrated out can be additionally suppressed, by factors of order k^2 M^d, where k is the bulk gravitational coupling. In the special case of a codimension-2 brane in a 6D supersymmetric bulk we also estimate the size of the contributions of short-wavelength bulk loops near the brane, and find these can be similarly suppressed.