Relating the cosmological constant and supersymmetry breaking in warped compactifications of IIB string theory

Abstract

It has been suggested that the observed value of the cosmological constant is related to the supersymmetry breaking scale M susy through the formula ⌳ϳM p 4 (M susy /M p ) 8 . We point out that a similar relation naturally arises in the codimension two solutions of warped spacetime varying compactifications of string theory, in which nonisotropic stringy moduli induce a small but positive cosmological constant. DOI: 10.1103/PhysRevD.67.041901 PACS number͑s͒: 11.25.Mj, 11.10.Kk, 98.80.Cq Recently, we addressed the question of whether de Sitter space ͓1͔ can be obtained from string theory ͓2͔. Such nonsingular, nonstatic spacetimes fall into the class of codimension two nonsupersymmetric string vacua studied in Refs. ͓3, 4, 5͔.1 In these models, supersymmetry is explicitly broken by a global cosmic brane ͓6͔ with a core of size ᐉ, extended along the DϪ2 ''longitudinal'' directions. While Refs. ͓3, 4, 5͔ considered a flat Minkowski brane, the main point of Ref.͓2͔ is the existence of nonsupersymmetric codimension two solutions with a positive cosmological constant, ⌳ b , in the (DϪ2)-dimensional longitudinal space. 2Since the cosmological constant in our model ͓2͔ is directly related to the nonisotropy of matter, we may compare it with various attempts to incorporate Mach's principle in string theory ͓8,9͔ as well with the idea that supersymmetry breaking might have a cosmological origin ͓10,11͔. In particular, it has been suggested that the observed value of the cosmological constant, ⌳ 4 ϳ10 Ϫ44 GeV 4 ͓12,13,7͔, may be related to the supersymmetry breaking scale M susy through the formula ͓14,15,10͔with M susy ϳ10 TeV and M p ϳ10 19 GeV as appropriate in four dimensions. 3 It is the aim of this work to point out that the setup of Ref. ͓2͔ for Dϭ6 leads naturally to a relation analogous to Eq. ͑1͒. In particular, the stringy moduli induce a nontrivial relation between the scale of the global cosmic brane, ᐉ, the nonisotropy of matter, , induced by the brane, and ⌳ b ͓2͔. We take this observation one step further and find an explicit relation between ⌳ b , ᐉ, and the natural mass scales in this theory, M 6 and M 4 -the Planck scales in the bulk and along the brane, respectively, thus deriving an equation analogous to Eq. ͑1͒.Although the detailed physics leading to this relation is unclear, we find it very intriguing that an equation similar to Eq. ͑1͒ emerges naturally in our framework. Still, one of the most important unresolved questions in the scenario presented in Ref. ͓2͔ is the issue of the stability of this nonsupersymmetric background in the full string theory. Since supersymmetry is broken, one also has to address the effects of stringy corrections. We will argue that those corrections are negligible.The general framework of our analysis is as in Refs. ͓3, 4, 5,2͔, to which we refer the reader for a more detailed analysis. Although we will be mostly interested in the phenomenologically relevant case in which Dϭ6, and hence the uncompactified spacetime is DϪ2ϭfour dimensional, we find it useful to work...

Probing naked singularities in non-supersymmetric string vacua

“…Recall that the general perturbation of the metric g µν → g µν + h µν satisfies (in a suitable gauge) the Lichnerowicz equation [50] ∆ L h µν = [δ The general perturbation is split into scalar, vector and tensor modes and the stability analysis is reduced to finding whether there exist any unstable modes for the perturbation. Work along these lines is in progress [51].…”

“…The distance from the naked singularity to these limits grows exponentially, but remains finite for all finite energies. By comparison, there is no 'outer' turning point for higher codimension brane probes [36,47]: there the velocity is constant and an outgoing brane probe would leave the singularity forever. Obviously, this distinction happens because, unlike its higher codimension analogues, Z 7 (r) has no asymptotic region and in fact diverges at r = ∞.…”

“…(While there does exist an analogous 'band' of allowed brane probe energies in the higher codimension case, its lower limit is constant [47].) It is of course possible to choose the constant dual-axion field strength so that the lower limit on the total energy of the brane probe would vanish at any particular point of interest:…”

“…Finally, even the perhaps somewhat curious looking region of allowed energies (3.29) can also be derived [47] from the standard analysis of supersymmetric 7-branes [36].…”

Exploring de Sitter space and holography

“…One approach to Euclidean de Sitter space was suggested in [2]. Various discussions of de Sitter space in the context of supergravity can be found in [21,22,23,24,25,26,27,28,29,31,30]. Related developments in the the study of time dependent backgrounds of string theory include recent work on spacelike brane solutions [32], space-time orbifolds with fixed planes that are localized in time [33], and Sen's proposal that dynamical rolling of the tachyon of open string field theory can lead to interesting consmologies [34].…”