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.
Highlights
Another set of swampland conjectures has to do with compactifications to spaces with non-zero cosmological constant
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 compactification volume
This allows us to split the various terms in the full quantum equations of motion according to their scalings, which in turn allows us to determine whether the equation of motion may be truncated, and whether a given putative solution resides within the EFT regime that defines the trans-series expansion in the first place
Summary
Consider a theory with degrees of freedom φi described by a full quantum effective action S[φi]. The equations of motion coming from this action give the fully non-perturbative behavior of the on-shell observables This theory can be taken to an asymptotic regime defined by a set of parameters gk → 0 and we can attempt to expand the full action around that point in the following way:. We will assume that this is the case, so that (2.1) and (2.2) are mathematically rigorous representations of the fully quantum corrected action and equations of motion, respectively This is not a wild assumption, since pretty much all the functions that appear in physics admit a trans-series representation, which is unique once a choice of expansion parameters is fixed. The full untruncated trans-series expression remains well-defined for all values of the expansion parameters even well outside any regime where truncation is possible, and represents the full quantum effective action S
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