Fine-tuning with Brane-Localized Flux in 6D Supergravity

TL;DR

This paper critically examines a proposed mechanism in 6D supergravity models to address the cosmological constant problem, finding that only scale-invariant flux couplings can avoid fine-tuning, which challenges previous claims.

Contribution

It demonstrates that flux couplings preserving scale invariance are necessary for a flat 4D geometry, showing that the original mechanism does not work as intended without scale invariance breaking.

Findings

Scale-invariant flux coupling guarantees flat on-brane geometry.

Weinberg's fine-tuning argument applies unless scale invariance is broken.

Breaking scale invariance may allow tuning to be avoided, explored in a companion paper.

Abstract

There are claims in the literature that the cosmological constant problem could be solved in a braneworld model with two large (micron-sized) supersymmetric extra dimensions. The mechanism relies on two basic ingredients: First, the cosmological constant only curves the compact bulk geometry into a rugby shape while the 4D curvature stays flat. Second, a brane-localized flux term is introduced in order to circumvent Weinberg's fine-tuning argument, which otherwise enters here through a backdoor via the flux quantization condition. In this paper, we show that the latter mechanism does not work in the way it was designed: The only localized flux coupling that guarantees a flat on-brane geometry is one which preserves the scale invariance of the bulk theory. Consequently, Weinberg's argument applies, making a fine-tuning necessary again. The only remaining window of opportunity lies within scale invariance breaking brane couplings, for which the tuning could be avoided. Whether the corresponding 4D curvature could be kept under control and in agreement with the observed value will be answered in our companion paper [arXiv:1512.03800].