Integer Conformal Dimensions for Type IIA Flux Vacua

Understand

We give a concise argument that supersymmetric AdS type IIA DGKT flux vacua on general Calabi-Yaus have, interpreted holographically, integer conformal dimensions for low-lying scalar primaries in the dual CFT.

• These integers are independent of any compactification details, such as the background fluxes or triple intersection numbers of the compact manifold.
• For the K\"ahler moduli and dilaton, there is one operator with $\Delta = 10$ and $h^{1,1}_{-}$ operators with $\Delta =6$, whereas the corresponding axions have $\Delta = 11$ and $\Delta = 5$.
• For the complex structure moduli, the $h^{2,1}$ saxions have $\Delta =2$, and the axions $\Delta =3$.