DGKT vacua satisfy the holographic cubic coupling constraint if and only if the Calabi-Yau threefold is rigid (h^{2,1}=0).
On the Conformal Field Theory Duals of type IIA AdS_4 Flux Compactifications
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abstract
We study the conformal field theory dual of the type IIA flux compactification model of DeWolfe, Giryavets, Kachru and Taylor, with all moduli stabilized. We find its central charge and properties of its operator spectrum. We concentrate on the moduli space of the conformal field theory, which we investigate through domain walls in the type IIA string theory. The moduli space turns out to consist of many different branches. We use Bezout's theorem and Bernstein's theorem to enumerate the different branches of the moduli space and estimate their dimension.
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A holographic consistency condition derived from large-N factorization requires vanishing cubic couplings for extremal-dimension operators and is non-trivially satisfied in DGKT AdS4 string vacua.
Holographic constraint on AdS vacua is violated for Z2 orbifolds but restored by non-abelian extensions, implying O-planes cannot wrap cycles in distinct homology classes.
Cancellations that satisfy a holographic three-point function constraint in DGKT vacua persist across examples with h^{2,1}=0 and more complicated triple-intersection numbers.
citing papers explorer
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$\mathcal{N}=1$ spectra, cubic couplings and the rigid fate of DGKT
DGKT vacua satisfy the holographic cubic coupling constraint if and only if the Calabi-Yau threefold is rigid (h^{2,1}=0).
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Broken and restored: a holographic constraint for AdS vacua with orbifolds
Holographic constraint on AdS vacua is violated for Z2 orbifolds but restored by non-abelian extensions, implying O-planes cannot wrap cycles in distinct homology classes.
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A note on the holographic consistency of DGKT-type vacua with $h^{2,1}=0$
Cancellations that satisfy a holographic three-point function constraint in DGKT vacua persist across examples with h^{2,1}=0 and more complicated triple-intersection numbers.