Conformal Brane World and Cosmological Constant

TL;DR

This paper explores a brane-world model where bulk supersymmetry constrains the brane's cosmological constant and conformal invariance, highlighting the necessity of conformal matter for consistent coupling.

Contribution

It demonstrates that in a conformal brane-world setup with bulk supersymmetry, the brane's cosmological constant and conformal invariance are protected.

Findings

Bulk supersymmetry prevents non-zero brane cosmological constant.

Consistent matter-gravity coupling requires the brane theory to be conformal.

Bulk supersymmetry safeguards both cosmological constant and conformal invariance.

Abstract

We consider a recently proposed setup where a codimension one brane is embedded in the background of a smooth domain wall interpolating between AdS and Minkowski minima. Since the volume of the transverse dimension is infinite, bulk supersymmetry is intact even if brane supersymmetry is completely broken. On the other hand, in this setup unbroken bulk supersymmetry is incompatible with non-zero brane cosmological constant, so the former appears to protect the latter. In this paper we point out that, to have a consistent coupling between matter localized on the brane and bulk gravity, in this setup generically it appears to be necessary that the brane world-volume theory be conformal. Thus, unbroken bulk supersymmetry appears to actually protect not only the cosmological constant but also conformal invariance on the brane.