Abstract
We observe that racetrack models for moduli stabilization are in tension with strong forms of the Weak Gravity Conjecture (WGC). Moreover, recently, it was noted that controlled KKLT-type de Sitter vacua seem to require a racetrack fine-tuning of the type introduced by Kallosh and Linde. We combine these observations and conclude that the quests for realizing parametrically large axion decay constants and controlled de Sitter vacua are intimately related. Finally, we discuss possible approaches to curing the conflict between the racetrack scheme and the WGC.
Highlights
Uplifting AdS vacua to dS vacua is argued to be possible when an AdS vacuum sits in the minimum of a sharply peaked potential and if there exist SUSY-breaking terms whose moduli-dependence is slowly varying compared with the sharply peaked AdS potential
In the rest of the paper we argue that such models can be challenged from two independent directions: 1. Given the racetrack alignment of the dual Coxeter numbers of the gauge groups, a ≈ b, for reasonable values of the parameters W0, A, B, any reasonably strong form of the weak gravity conjecture (WGC) [14] is violated, which some believe to be a fundamental principle of quantum gravity: a parametrically long axion direction emerges
It is believed that some form of the weak gravity conjecture (WGC) [14] holds in all consistent effective field theories that arise as the low energy limit of a genuine string compactification
Summary
Uplifting AdS vacua to dS vacua is argued to be possible when an AdS vacuum sits in the minimum of a sharply peaked potential and if there exist SUSY-breaking terms whose moduli-dependence is slowly varying compared with the sharply peaked AdS potential. A possible source for two such exponential terms as the leading order non-perturbative effects are gaugino condensates on two stacks of D7 branes wrapping 4-cycles in the same homology class but at sufficiently large distances such that the gauge group induced by the 7-brane stacks factorizes The reason that such models are not contained in the nogo theorem is the possible existence of a fine-tuning of the cosmological constant in the SUSY AdS vacuum prior to uplift. There is a tuning of the coefficients A, B, a, b that brings the AdS vacuum energy to zero, while preserving finite masses for the T modulus In such a situation sufficiently small SUSY-breaking effects necessarily lead to dS vacua.
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