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Register a new userHidden Relations of Central Charges and OPEs in Holographic CFT
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It is known that the $(a,c)$ central charges in four-dimensional CFTs are linear combinations of the three independent OPE coefficients of the stress-tensor three-point function. In this paper, we adopt the holographic approach using AdS gravity as an effect field theory and consider higher-order corrections up to and including the cubic Riemann tensor invariants. We derive the holographic central charges and OPE coefficients and show that they are invariant under the metric field redefinition. We further discover a hidden relation among the OPE coefficients that two of them can be expressed in terms of the third using differential operators, which are the unit radial vector and the Laplacian of a four-dimensional hyperbolic space whose radial variable is an appropriate length parameter that is invariant under the field redefinition. Furthermore, we prove that the consequential relation $c=1/3 ell_{rm eff}partial a/partialell_{rm eff}$ and its higher-dimensional generalization are valid for massless AdS gravity constructed from the most general Riemann tensor invariants.
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We explore the structure of holographic entropy relations (associated with information quantities given by a linear combination of entanglement entropies of spatial sub-partitions of a CFT state with geometric bulk dual). Such entropy relations can be recast in multiple ways, some of which have significant advantages. Motivated by the already-noted simplification of entropy relations when recast in terms of multipartite information, we explore additional simplifications when recast in a new basis, which we dub the K-basis, constructed from perfect tensor structures. For the fundamental information quantities such a recasting is surprisingly compact, in part due to the interesting fact that entropy vectors associated to perfect tensors are in fact extreme rays in the holographic entropy cone (as well as the full quantum entropy cone). More importantly, we prove that all holographic entropy inequalities have positive coefficients when expressed in the K-basis, underlying the key advantage over the entropy basis or the multipartite information basis.
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We propose a new non-holographic formulation of AdS/CFT correspondence, according to which quantum gravity on AdS and its dual non-gravitational field theory both live in the same number D of dimensions. The field theory, however, appears (D-1)-dimensional because the interactions do not propagate in one of the dimensions. The D-dimensional action for the field theory can be identified with the sum over (D-1)-dimensional actions with all possible values $Lambda$ of the UV cutoff, so that the extra hidden dimension can be identified with $Lambda$. Since there are no interactions in the extra dimension, most of the practical results of standard holographic AdS/CFT correspondence transcribe to non-holographic AdS/CFT without any changes. However, the implications on black-hole entropy change significantly. The maximal black-hole entropy now scales with volume, while the Bekenstein-Hawking entropy is interpreted as the minimal possible black-hole entropy. In this way, the non-holographic AdS/CFT correspondence offers a simple resolution of the black-hole information paradox, consistent with a recently proposed gravitational crystal.
Following recent work on heavy-light correlators in higher-dimensional conformal field theories (CFTs) with a large central charge $C_T$, we clarify the properties of stress tensor composite primary operators of minimal twist, $[T^m]$, using arguments in both CFT and gravity. We provide an efficient proof that the three-point coupling $langle mathcal{O}_Lmathcal{O}_L [T^m]rangle$, where $mathcal{O}_L$ is any light primary operator, is independent of the purely gravitational action. Next, we consider corrections to this coupling due to additional interactions in AdS effective field theory and the corresponding dual CFT. When the CFT contains a non-zero three-point coupling $langle TT mathcal{O}_Lrangle$, the three-point coupling $langle mathcal{O}_Lmathcal{O}_L [T^2]rangle$ is modified at large $C_T$ if $langle TTmathcal{O}_L rangle sim sqrt{C_T}$. This scaling is obeyed by the dilaton, by Kaluza-Klein modes of prototypical supergravity compactifications, and by scalars in stress tensor multiplets of supersymmetric CFTs. Quartic derivative interactions involving the graviton and the light probe field dual to $mathcal{O}_L$ can also modify the minimal-twist couplings; these local interactions may be generated by integrating out a spin-$ell geq 2$ bulk field at tree level, or any spin $ell$ at loop level. These results show how the minimal-twist OPE coefficients can depend on the higher-spin gap scale, even perturbatively.
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