DGKT vacua satisfy the holographic cubic coupling constraint if and only if the Calabi-Yau threefold is rigid (h^{2,1}=0).
Extremal Correlators in the AdS/CFT Correspondence
5 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The non-renormalization of the 3-point functions $tr X^{k_1} tr X^{k_2} tr X^{k_3}$ of chiral primary operators in N=4 super-Yang-Mills theory is one of the most striking facts to emerge from the AdS/CFT correspondence. A two-fold puzzle appears in the extremal case, e.g. k_1 = k_2 + k_3. First, the supergravity calculation involves analytic continuation in the k_i variables to define the product of a vanishing bulk coupling and an infinite integral over AdS. Second, extremal correlators are uniquely sensitive to mixing of the single-trace operators $tr X^k$ with protected multi-trace operators in the same representation of SU(4). We show that the calculation of extremal correlators from supergravity is subject to the same subtlety of regularization known for the 2-point functions, and we present a careful method which justifies the analytic continuation and shows that supergravity fields couple to single traces without admixture. We also study extremal n-point functions of chiral primary operators, and argue that Type IIB supergravity requires that their space-time form is a product of n-1 two-point functions (as in the free field approximation) multiplied by a non-renormalized coefficient. This non-renormalization property of extremal n-point functions is a new prediction of the AdS/CFT correspondence. As a byproduct of this work we obtain the cubic couplings $t \phi \phi$ and $s \phi \phi$ of fields in the dilaton and 5-sphere graviton towers of Type IIB supergravity on $AdS_5 \times S^5$.
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background 2representative citing papers
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 Schwinger pair creation generates nonlocal magic for spacetime dimensions d>2, as shown by a non-flat entanglement spectrum that can be read from the probe brane free energy.
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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A Holographic Constraint on Scale Separation
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.
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The nonlocal magic of a holographic Schwinger pair
Holographic Schwinger pair creation generates nonlocal magic for spacetime dimensions d>2, as shown by a non-flat entanglement spectrum that can be read from the probe brane free energy.
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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.