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A bstract It is a long-standing conjecture that any CFT with a large central charge and a large gap ∆ gap in the spectrum of higher-spin single-trace operators must be dual to a local effective field theory in AdS. We prove a sharp form of this conjecture by deriving numerical bounds on bulk Wilson coefficients in terms of ∆ gap using the conformal bootstrap. Our bounds exhibit the scaling in ∆ gap expected from dimensional analysis in the bulk. Our main tools are dispersive sum rules that provide a dictionary between CFT dispersion relations and S-matrix dispersion relations in appropriate limits. This dictionary allows us to apply recently-developed flat-space methods to construct positive CFT functionals. We show how AdS 4 naturally resolves the infrared divergences present in 4D flat-space bounds. Our results imply the validity of twice-subtracted dispersion relations for any S-matrix arising from the flat-space limit of AdS/CFT.
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This content will become publicly available on December 1, 2025
Universal bounds on CFT Distance Conjecture
A<sc>bstract</sc> For any unitary conformal field theory in two dimensions with the central chargec, we prove that, if there is a nontrivial primary operator whose conformal dimension ∆ vanishes in some limit on the conformal manifold, the Zamolodchikov distancetto the limit is infinite, the approach to this limit is exponential ∆ = exp(−αt+O(1)), and the decay rate obeys the universal boundsc−1/2≤α≤ 1. In the limit, we also find that an infinite tower of primary operators emerges without a gap above the vacuum and that the conformal field theory becomes locally a tensor product of a sigma-model in the large radius limit and a compact theory. As a corollary, we establish a part of the Distance Conjecture about gravitational theories in three-dimensional anti-de Sitter space. In particular, our bounds onαindicate that the emergence of exponentially light states is inevitable as the moduli field corresponding totrolls beyond the Planck scale along the steepest path and that this phenomenon can begin already at the curvature scale of the bulk geometry. We also comment on implications of our bounds for gravity in asymptotically flat spacetime by taking the flat space limit and compare with the Sharpened Distance Conjecture.
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- Award ID(s):
- 2210420
- PAR ID:
- 10632426
- Publisher / Repository:
- Springer Nature
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2024
- Issue:
- 12
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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