Effective Theories as Truncated Trans-Series and Scale Separated Compactifications

Abstract

We study the possibility of realizing scale-separated type IIB Anti-de Sitter and de Sitter compactifications within a controlled effective field theory regime defined by low-energy and large (but scale-separated) compactification volume. The approach we use views effective theories as truncations of the full quantum equations of motion expanded in a trans-series around this asymptotic regime. By studying the scalings of all possible perturbative and non-perturbative corrections we identify the effects that have the right scaling to allow for the desired solutions. In the case of Anti-de Sitter, we find agreement with KKLT-type scenarios, and argue that non-perturbative brane-instantons wrapping four-cycles (or similarly scaling effects) are essentially the only ingredient that allows for scale separated solutions. We also comment on the relation of these results to the AdS swampland conjectures. For the de Sitter case we find that we are forced to introduce an infinite number of relatively unsuppressed corrections to the equations of motion, leading to a breakdown of effective theory. This suggests that if de Sitter vacua exist in the string landscape, they should not be thought of as residing within the same effective theory as the AdS or Minkowski compactifications, but rather as defining a separate asymptotic regime, presumably related to the others by a duality transformation.

arXiv comment24 pages, v2 changes to the scaling analysis in section 3.4, references added

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• Four-dimensional de Sitter space is a Glauber-Sudarshan state in string theory
• Three-dimensional flux vacua from IIB on co-calibrated G2 orientifolds
• O6-plane backreaction on scale-separated Type IIA AdS${}_3$ vacua
• AdS scale separation and the distance conjecture
• Resurgence of a de Sitter Glauber-Sudarshan State: Nodal Diagrams and Borel Resummation
• Contracting Cosmologies and the Swampland
• How a four-dimensional de Sitter solution remains outside the swampland
• Deriving the Gibbons-Maldacena-Nunez no-go theorem from the Raychaudhuri equation
• What if string theory has a de Sitter excited state?
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme