On scale separation in type II AdS flux vacua

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 N = 1 supersymmetric models which have a 10d lifting to a compactification on S 3 × S 3 .We show how using KK scales properly modified by the compact metric leads to no separation of scales with M 2 KK = c|Λ|, with 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 analysis seems 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 × S 3 . In this geometric dual one again observes that the strong AdS distance conjecture is obeyed with M 2 KK = c ′ |Λ|, 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 KK = c|Λ| with c a fluxindependent numerical constant.

On supersymmetric AdS4 orientifold vacua

“…In particular here we can consider Im Ω as a perturbation over Im Ω CY , and apply the perturbation formulas [35, (3. From the definition of ϕ it is easy to see that X 6 ϕ = 0 and therefore e −4A = 1 up to this order of approximation, as expected. This moreover leads to 5) and so, since dK = 0, the Bianchi identity dH = 0 is satisfied up to order O(g 3 s ). Finally, when plugging (6.5) into (4.9a) we obtain that dB = 2µg s K + O(g 2 s ), consistently with our assumption.…”

“…Let us consider type IIA string theory compactified in an orientifold of X 4 × X 6 with X 6 a compact real six-manifold with a Calabi-Yau metric, and therefore a Kähler 2-form J CY and a holomorphic 3-form Ω CY . Following the standard construction [24], we take the orientifold action to be generated by Ω p (−1) F L R, 5 with R an anti-holomorphic involution acting as RJ CY = −J CY and RΩ CY = −Ω CY . The fixed locus Π O6 of R is one or several 3-cycles of X 6 in which O6-planes are located.…”

“…This means JHEP08(2020)087 that the solutions are not really d-dimensional in any physical sense: physics looks tenor eleven-dimensional to a hypothetical observer. There have been many studies of the property of scale separation in string theory, see in particular [1][2][3][4][5][6].…”

O‐Plane Backreaction and Scale Separation in Type IIA Flux Vacua

“…Recently, there has been a renewed interest in the question whether string theory admits AdS solutions with scale separation (see, e.g., [15,13,32,33]). In [13], it was conjectured that AdS vacua in the limit Λ → 0 satisfy M ∼ |Λ| α (6.1)…”

“…We thus find M KK ∼ h 1/2 /V 1/(10−d) ∼ m 0 h 0 in string units. 33 The d-dimensional scalar curvature scales like R d = R µν g µν ∼ m 0 h 0 , again in string units. 34 This yields…”