Abstract
Maximally symmetric curved-brane solutions are studied in dilatonic braneworld models which realise the self-tuning of the effective four-dimensional cosmological constant. It is found that no vacua in which the brane has de Sitter or anti-de Sitter geometry exist, unless one modifies the near-boundary asymptotics of the bulk fields. In the holographic dual picture, this corresponds to coupling the UV CFT to a curved metric (possibly with a defect). Alternatively, the same may be achieved in a flat-space QFT with suitable variable scalar sources. With these ingredients, it is found that maximally symmetric, positive and negative curvature solutions with a stabilised brane position generically exist. The space of such solutions is studied in two different types of realisations of the self-tuning framework. In some regimes we observe a large hierarchy between the curvature on the brane and the boundary UV CFT curvature. This is a dynamical effect due to the self-stabilisation mechanism. This setup provides an alternative route to realising de Sitter space in string theory.
Highlights
Given a dual interpretation in terms of a strongly coupled, large-N, four-dimensional field theory
The class of solutions we find here in the context of holography offer an alternative way of producing de Sitter, on the brane, compared to methods based on engineering bulk solutions, as was recently advocated in [44]
In this work we studied self-stabilising solutions of a 4-dimensional brane embedded into a 5-dimensional bulk, where the curvature of the brane is adjusted dynamically
Summary
We will consider Einstein-scalar theory in d + 1 dimensions, coupled to a d-dimensional dynamical hypersurface (brane). The simplest possibility to move in this direction is to look for a solution in which the curvature is due solely to the embedding of the brane, and the bulk geometry retains its four-dimensional Poincare invariance In this ansatz, the boundary conditions (which define the dual CFT data) are the same as those studied in [20]. In the rest of this paper we will explore the second option, and embed the brane as a static hypersurface in a bulk metric of the form (2.4), where ζμν is identified with the metric of the dual UV CFT These solutions are not unrelated to the first option described above: as we will discuss in more detail, a coordinate transformation can bring a solution of the form (2.4) to one of the form (2.11) with flat asymptotic conditions, at the cost of introducing a time- or space-dependence in the scalar field at leading order in the near-boundary expansion. In the holographic dual language, this situation describes a CFT living on flat space, but driven by a varying scalar source
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