Effective Theories as Truncated Trans-Series and Scale Separated Compactifications

TL;DR

This paper investigates the conditions under which scale-separated Anti-de Sitter and de Sitter compactifications can be realized within effective field theories derived from string theory, highlighting the role of non-perturbative effects and the limitations for de Sitter solutions.

Contribution

It introduces a trans-series framework to analyze scale-separated compactifications and identifies key effects necessary for their realization, especially in the Anti-de Sitter case.

Findings

Non-perturbative brane-instantons are crucial for AdS scale separation.

De Sitter solutions require an infinite number of unsuppressed corrections.

Effective theories break down for de Sitter vacua, implying they may lie outside the same regime as AdS solutions.

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.