The Boundaries of KKLT

Abstract

We consider the conundrum of generating de Sitter space from higher-dimensional geometry, with particular attention to KKLT-type constructions [3] and their 5d implications. We show that even in the probe approximation with small g s , a consistent higher-dimensional solution requires a deformation of a modulus field playing the role of a Goldberger-Wise stabilizing field in Randall-Sundrum type geometries that occurs through a shift in a the throat length. We identify the light radion field that sets the length of the throat, whose origin is the dynamical conifold deformation parameter. By analyzing the theory as a 5d model of mismatched branes in AdS5 space with a GW stabilization mechanism, we show how energy (and supersymmetry breaking) is transferred to both the IR and UV regions of the throat to generate a consistent 4d de Sitter sliced geometry. This should help resolve some of the recent apparent paradoxes in explicit higher-dimensional constructions. Moreover, the radion gives insight into the potential for the previously identified "conifold instability". We argue that this instability would be a destabilization of the potential for the radion in KKLT, which can occur when the perturbation is too large. If indeed √ g s M is too small, the radion would enter on its runaway direction and the conifold deformation would shrink to zero size. It is difficult to satisfy the required bound and a) maintain a hierarchy in the simpler CY manifolds and b) complete the cosmological phase transition into the stabilized throat, We also discuss the implications of this type of setup for supersymmetry breaking, and how multiple throats can introduce hierarchies of supersymmetry breaking masses, even in an anomaly-mediated scenario. In an appendix we consider general compactification constraints.

Nothing really matters

“…Particularly due to their simplicity, the instanton geometries presented here represent useful toy-models to extend the study of "braneworld" observers living on "nothing" [41]. This philosophy is in line with a novel interpretation of stringy dS vacua constructed by using infinite throats [42].…”

Geometries with mismatched branes

“…This can be accomplished by either directly affecting the brane tensions, or by affecting the bulk cosmological constant (which sets λ c ). For a detailed discussion of the viability of KKLT and the insights one can glimpse from rephrasing it in the language of an RS construction see [9].…”

“…(5.3) 9 We found it convenient to rescale the field ϕRS of [19] by a factor of √ 12κ with κ = 2M 3 5 /k = (16πG) −1 in order to have an overall factor of κ 2 in front of the action rather than a canonically normalized scalar as in their work.…”

“…Recently RS brane worlds have been employed to understand the evaporation of black holes [3,4] in the context of the AdS/BCFT correspondence [5][6][7]. RS branes also play a crucial role in realizing accelerating universes in string theory, both the classic KKLT construction [8,9] as well as in the recent proposals of [10][11][12]. In particular in the latter context one question that has been raised is that of "mismatched" branes.…”

Classical de Sitter solutions in three dimensions without tachyons?

“…Although this is still somewhat unclear and preliminary results can be found in [82,83]. Interestingly other compactification effects exist on stability when throats are inserted in compact spaces, see for instance [61,[84][85][86][87].…”