On stringy de Sitter spacetimes

Abstract

We reexamine a family of models with a 3+1-dimensional de Sitter spacetime obtained in the standard tree-level low-energy limit of string theory with a non-trivial anisotropic axion-dilaton background. While such limiting approximations are encouraging but incomplete, our analysis reveals a host of novel features, and shows these models to relate standard and well understood supersymmetric string theory solutions. Finally, we conjecture that this de Sitter spacetime naturally arises by including more of the stringy degrees of freedom, such as a recently advanced variant of the non-commutative phasespace formalism, as well as the analytic continuation of a complex two-dimensional Fano variety arising as a small resolution in a Calabi-Yau 5-fold.

Open Problems on Classical de Sitter Solutions

“…We assume that for each source, these 1-forms split into two sets {e a || } and {e a ⊥ }, that are globally distinct. This means that the structure group of the cotangent bundle is reduced from O (6) to O( p − 3) × O(9 − p), or a subgroup thereof. Note that no assumption is made on the coordinate dependence.…”

“…For instance, this not the case in isotropic spheres, but it can easily be achieved in nilmanifolds: as can be seen in (5.5), taking the fiber radius small compared to the base ones, r 3 r 1 , r 2 , generates a hierarchy, eventually leading to a small N 2 f . 6 Secondly, R 6 is a linear combination of squares of structure constants, where positive and negative contributions could be tuned and almost cancel each other, giving eventually a small but non-vanishing value. Using the general expression (4.17) of R 6 on group manifolds with the parameter λ (3.3) (see (3.35)), we could not bound −R 6 from below by a single positive term, i.e.…”

“…Several possible loopholes were however mentioned in [41]. The most relevant one to us is the fact that, 6 For M = Nil 3 × T 3 , one has R 6 = − 1 2 ( f 3 12 ) 2 . When all radii except r 3 are equal to R, one computes N 2 f = (r 3 /R) 7 3 N i f 2 /2.…”

“…Beyond the cosmological motivation, this is an interesting question per se, with other applications such as holography and the relation to higher spin theories. In this paper we address this question restricting ourselves to classical perturbative de Sitter string backgrounds, discarding other approaches [2,3] that involve string loop or non-perturbative contributions, α corrections, or further ingredients (more recent proposals include [4][5][6] ). A motivation for our restrictive setting is that it is simpler, the approximations required to reach a final effective theory are a priori easier to control.…”

T-branes and G2 backgrounds

“…3 It seems possible that some of the fibers in the deformation family of [16] could acquire such point-like singularities, however as of now there is no technique available to probe them. Compact G 2 's with point-like 1 In F-theory, there has recently been renewed interest in the use of Spin(7) backgrounds as a way to generate novel models of dark energy [2,3] (see also [4][5][6][7]). Though less studied, F-theory on G 2 backgrounds should also lead to novel 5D vacua [8].2 In the non-compact case, there are quite a few known examples of conical G 2 -manifolds.…”