Near-Extremal Correlators and Generalized Consistent Truncation for AdS_{4|7}\times S^{7|4}

Abstract

We present conjectures for the space-time form and leading large N dependence of extremal and near-extremal correlation functions in the \N=8 superconformal Yang-Mills theory in d=3 as well as in the (0,2) superconformal theory in d=6, using their gravity duals with M-theory on $Ad{S}_4\times {\S }^7$ and $Ad{S}_7\times {\S }^4$ respectively. As a key part of the conjectures, we argue that the bulk couplings associated with extremal and near-extremal field configurations in the corresponding $Ad{S}_4$ and $Ad{S}_7$ gauged supergravities vanish. The vanishing of these couplings constitutes a generalization of the property of consistent truncation of the Kaluza-Klein modes.

22 pages, 2 figures

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• OPEs and 3-point correlators of protected operators in N=4 SYM
• On Superconformal Four-Point Mellin Amplitudes in Dimension $d>2$
• Supergravity one-loop corrections on AdS_7 and AdS_3, higher spins and AdS/CFT
• Implications of Superconformal Symmetry for Interacting (2,0) Tensor Multiplets
• Three-Point Functions of Quarter BPS Operators in N=4 SYM
• Universal properties of superconformal OPEs for 1/2 BPS operators in $3\le D\le 6$
• Conformal anomaly c-coefficients of superconformal 6d theories
• Holography and Quaternionic Taub-NUT
• Negative scalar potentials and the swampland: an Anti-Trans-Planckian Censorship Conjecture
• Fermi surface behavior in the ABJM M2-brane theory
• Double-Trace Flows and the Swampland
• Representations of superconformal algebras in the AdS_7/4/CFT_6/3 correspondence
• Characters of the Positive Energy UIRs of D=4 Conformal Supersymmetry
• AdS/SCFT in Superspace
• Conformal superfields and BPS states in AdS_4/7 geometries
• Revisiting Extremal Couplings in AdS/CFT
• Dual Instantons in Anti-membranes Theory
• Marginal Fluctuations as Instantons on M2/D2-Branes
• Massive (pesudo)Scalars in AdS${}_4$, SO(4) Invariant Solutions and Holography
• Spin Structures and AdS${}_4$ Holography
• Higgs-like (pseudo)Scalars in AdS${}_4$, Marginal and Irrelevant Deformations in CFT_3 and Instantons on S^3
• 11D Supergravity on $Ad{S}_4\times S^7$ versus $Ad{S}_7\times S^4$