Integer Conformal Dimensions for Type IIA Flux Vacua

TL;DR

This paper demonstrates that supersymmetric AdS flux vacua in type IIA string theory exhibit universal integer conformal dimensions for certain scalar operators in the dual CFT, independent of compactification details.

Contribution

It provides a concise argument that these integer conformal dimensions are universal features of the dual CFTs for type IIA flux vacua, regardless of specific compactification parameters.

Findings

Scalar operators have integer conformal dimensions: Δ=10, 6, 11, 5, 2, 3.

Dimensions are independent of fluxes and intersection numbers.

Discussion on the origin and potential modifications of these integers.

Abstract

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 $\Delta =3$. We give a tentative discussion of the origin of these integers and effects that would modify these results.