On scale separation in type II AdS flux vacua

TL;DR

This paper investigates the relationship between AdS and Kaluza-Klein scales in type II flux vacua, demonstrating that proper scale definitions align with the AdS distance conjecture and reveal a universal flux-independent scale relation.

Contribution

It clarifies how to correctly define KK scales in flux compactifications, showing they obey a universal relation with the cosmological constant, consistent with the AdS distance conjecture.

Findings

Properly defined KK scales satisfy $M^2_{KK} = ext{constant} imes | ext{Lambda}|$

Naive effective theory applications can violate the AdS distance conjecture

The universal scale relation holds across different flux models and dualities.

Abstract

We study the separation of AdS and Kaluza-Klein (KK) scales in type II 4d AdS orientifold vacua. We first address this problem in toroidal/orbifold type IIA vacua with metric fluxes, corresponding to compactifications in twisted tori, both from the 4d and 10d points of view. We show how the naive application of the effective 4d theory leads to results which violate the AdS distance conjecture, in a class of $\mathcal{N}=1$ supersymmetric models which have a 10d lifting to a compactification on $S^3\times S^3$. We show how using KK scales properly modified by the compact metric leads to no separation of scales with $M^2_{\text{KK}} = \mathfrak{c} |\Lambda|$, with $\mathfrak{c}$ a numerical constant independent of fluxes. This applies with no need to keep non-leading fluxes fixed. We also consider a class of IIB models with non-geometric fluxes in which the effective field theory analysisseems to lead to a naive separation of scales and a violation of the AdS distance conjecture. It has a T-dual which again may be understood as a 10d type IIA theory compactified on $S^3\times S^3$. In this geometric dual one again observes that the strong AdS distance conjecture is obeyed with $M^2_{\text{KK}} = \mathfrak{c}' |\Lambda|$, if one takes into account the curvature in the internal space. These findings seem to suggest that all toroidal/orbifold models with fluxes in this class obey $M^2_{\text{KK}} = \mathfrak{c} |\Lambda|$ with $\mathfrak{c}$ a flux-independent numerical constant.