Broken and restored: a holographic constraint for AdS vacua with orbifolds
Abstract
It has been suggested that families of weakly-coupled AdS vacua with a large-N holographic dual must satisfy non-trivial consistency requirements, which amount to the vanishing of certain cubic couplings, corresponding to (super-)extremal arrangements of scalar operators. While this constraint is known to hold in the simplest incarnation of the DGKT scenario in massive type IIA string theory, i.e. on the Z3× Z3 orbifold, we find that it is generically violated for type II AdS3 and AdS4 vacua arising from Z2 × Z2 × Z2 and Z2 × Z2 orbifolds respectively, including scale-separated solutions and DGKT-CFI-type models. In most cases, however, this can be cured by enlarging the orbifold group to a suitable (non-abelian) extension that projects out precisely those scalar operators that would otherwise participate in the constrained cubic couplings. Our results suggest that consistency of the putative holographic dual imposes a non-trivial restriction on the compactification geometry, indicating in particular that O-planes cannot wrap cycles in distinct homology classes.
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