A note on the magnitude of the flux superpotential

Abstract

The magnitude of the flux superpotential W flux plays a crucial role in determining the scales of IIB string compactifications after moduli stabilisation. It has been argued that values of W flux ≪ 1 are preferred, and even required for physical and consistency reasons. This note revisits these arguments. We establish that the couplings of heavy Kaluza-Klein modes to light states scale with the internal volume as g ∼ M KK /M P ∼ V −2/3 ≪ 1 and argue that consistency of the superspace derivative expansion requires gF/M 2 ∼ m 3/2 /M KK ≪ 1, where F is the auxiliary field of the light fields and M the ultraviolet cutoff. This gives only a mild constraint on the flux superpotential, W flux ≪ V 1/3 , which can be easily satisfied for O(1) values of W flux . This regime is also statistically favoured and makes the Bousso-Polchinski mechanism for the vacuum energy hierarchically more efficient.

Explicit de Sitter flux vacua for global string models with chiral matter

“…In order to have a consistent superspace derivative expansion in the 4D effective field theory, one requires V ≫ |W 0 | 3 [61]. This implies that the Kähler moduli have to be stabilised such that V ≫ 10 3 , respectively, V ≫ 10 6 depending on |W 0 |.…”

“…27 This is consistent with the following two important requirements necessary to trust the 4D low-energy theory. Firstly, we must have V ≫ |W 0 | 3 in order to control the superspace derivative expansion by having a gravitino mass smaller than the Kaluza-Klein scale M KK [61]. Secondly, we need V ≫ |W 0 | 6 to have a vacuum energy density smaller than M 4 KK [61,84,85].…”

Towards an explicit model of large field inflation

“…In lieu of an explicit geometry the estimates of mτ and m KK are only reliable up to order of magnitude, however an explicit calculation of moduli and Kaluza-Klein masses demonstrating that this model cannot obey the required hierarchy would serve as additional evidence for the swampland conjecture. However, this potential inconsistency in the hierarchy can also be avoided due to the fact that the coupling of the Kaluza-Klein modes to fields in the effective theory should be additionally suppressed by powers of the volume [33]. It is crucial to check this hierarchy where mτ and m KK can be reliably computed; given the current lack of an explicit geometry which accommodates our model, this is beyond the current scope of this work.…”

Dark radiation constraints on mixed Axion/Neutralino dark matter

“…Previous data from WMAP7, the South Pole Telescope (SPT) and the Atacama Cosmology Telescope (ACT) suggested N ef f ≃ 3.5 − 4.5 [36], indicating a source of dark radiation beyond the SM. A variety of papers have recently explored this possibility [37,38,39,40,35,41,42]. More recently, the ACT [43] has released additional data, which reduced the N ef f value combined with the measurement of baryon acoustic oscillations (BAO) and the Hubble constant to:…”