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].
Highlights
One class1 of models works with compact but large, viz. micron-sized, extra dimensions.2 The compact space has the topology of a sphere and closes in two infinitely thin three-branes situated at the north and south pole
We mainly focus on the supersymmetric large extra dimensions (SLED) model including the brane-localized flux (BLF) term
Two questions are at the core of our work: 1. What is the condition for exact 4D flatness in this model? It is clear that answering this question is of great interest with respect to the CC problem because we are looking for an explicit mechanism to hide the CC from a brane observer
Summary
We use Weinberg’s sign conventions [20]. Six dimensional spacetime coordinates are denoted by XM 3), and the two extra space dimensions are labeled by ym (m = 1, 2). √ density), i.e. its components are ±1/ g2. The delta function transforms as a density, so there is no metric determinant factor in its normalization condition d2y δ(2)(y) = 1
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