Broken and restored: a holographic constraint for AdS vacua with orbifolds

TL;DR

This paper investigates holographic constraints on AdS vacua with orbifolds, revealing that certain consistency conditions are violated in some models but can be restored by enlarging the orbifold group, thus constraining compactification geometry.

Contribution

It demonstrates that holographic consistency conditions are violated in many orbifold AdS vacua but can be restored through non-abelian orbifold extensions, impacting compactification geometry.

Findings

Known constraints hold for simple orbifolds like Z3×Z3 in massive IIA.

Violations occur in Z2×Z2×Z2 and Z2×Z2 orbifolds in AdS3 and AdS4 vacua.

Enlarging the orbifold group restores the constraints in most cases.

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 $\mathbb{Z}_3\times \mathbb{Z}_3$ orbifold, we find that it is generically violated for type II AdS$_3$ and AdS$_4$ vacua arising from $\mathbb{Z}_2 \times \mathbb{Z}_2 \times \mathbb{Z}_2$ and $\mathbb{Z}_2 \times \mathbb{Z}_2$ 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.