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Abstract:

We give a concise argument that supersymmetric anti–de Sitter type IIA DeWolfe-Giryavets-Kachru-Taylor flux vacua on general Calabi-Yau’s have, interpreted holographically, integer conformal dimensions for low-lying scalar primaries in the dual conformal field theory. These integers are independent of any compactification details, such as the background fluxes or triple intersection numbers of the compact manifold. For the Kähler moduli and dilaton, there is one operator with Δ=10 and h1,1− operators with Δ=6, whereas the corresponding axions have Δ=11 and Δ=5. For the complex structure moduli, the h2,1 saxions have Δ=2, and the axions Δ=3. We give a tentative discussion of the origin of these integers and effects that would modify these results.

Abstract:

We extend studies of holographic aspects of moduli stabilisation scenarios to both fibred versions of LVS and the type IIA DGKT flux vacua. We study the holographic properties of the low-energy moduli Lagrangian that describes both the AdS vacuum and also small perturbations about it. For type IIA vacua in the large-volume regime, the CFT data (operator dimensions and higher-point interactions) take a universal form independent of the many arbitrary flux choices, as was previously found for LVS stabilisation. For these IIA vacua the conformal dimensions of the dual operators are also, surprisingly, all integers, although we do not understand a deeper reason why this is so. In contrast to behaviour previously found for LVS and KKLT, the fibred models also admit cases of mixed double-trace operators (for two different axion fields) where the anomalous dimension is positive.