A note on the holographic consistency of DGKT-type vacua with $h^{2,1}=0$

Abstract

Recent works have pointed out the existence of a holographic constraint on (extremal) three-point functions of scalar moduli in scale-separated AdS vacua. Moreover, it has been shown that this constraint is satisfied in the DGKT scenario in massive type IIA for the original ${\mathbb{T}}^6/({\mathbb{Z}}_3\times {\mathbb{Z}}_3)$ orbifold, as a result of a series of unexpected cancellations. We extend the analysis to more elaborate scenarios, involving geometries with less symmetry and more complicated triple-intersection numbers. Surprisingly, the cancellations persist in all examples with $h^{2,1}=0$, leading us to speculate this conclusion might hold more generally.

16 pages plus appendices; v2: references added