AdS${}_4$/CFT${}_3$ for Unprotected Operators

Abstract

We consider the four-point function of the lowest scalar in the stress-energy tensor multiplet in $\mathcal{N}=8$ ABJ(M) theory \cite{Aharony:2008ug, Aharony:2008gk}. At large central charge $c_T\sim N^{3/2}$, this correlator is given by the corresponding holographic correlation function in 11d supergravity on $Ad{S}_4\times S^7$. We use Mellin space techniques to compute the leading $1/c_T$ correction to anomalous dimensions and OPE coefficients of operators that appear in this holographic correlator. For half and quarter-BPS operators, we find exact agreement with previously computed localization results. For the other BPS and non-BPS operators, our results match the $\mathcal{N}=8$ numerical bootstrap for ABJ(M) at large $c_T$, which provides a precise check of unprotected observables in AdS/CFT.

22 pages, 1 figure, v4, fixed typos

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• Algebraic structures on parallel M2-branes
• Holography from Conformal Field Theory
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• Conformal Bootstrap in Mellin Space
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• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Four point function of $\mathcal{N}=4$ stress-tensor multiplet at strong coupling
• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• Solving M-theory with the Conformal Bootstrap
• Holographic Four-Point Functions in the (2, 0) Theory
• M-theory Beyond The Supergravity Approximation
• Exploring Perturbative Conformal Field Theory in Mellin space

Cited by in corpus (22)

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• $20^{\prime }$ Five-Point Function from $Ad{S}_5\times S^5$ Supergravity
• Far Beyond the Planar Limit in Strongly-Coupled $\mathcal{N}=4$ SYM
• Genus-2 Holographic Correlator on $Ad{S}_5\times S^5$ from Localization
• $\mathbf{Ad}{\mathbf{S}}_3\times {\mathbf{S}}^3$ Tree-Level Correlators: Hidden Six-Dimensional Conformal Symmetry
• The M-Theory S-Matrix From ABJM: Beyond 11D Supergravity
• On Superconformal Four-Point Mellin Amplitudes in Dimension $d>2$
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• The M-theory Archipelago
• Holographic correlators in AdS${}_3$ without Witten diagrams
• ABJM at Strong Coupling from M-theory, Localization, and Lorentzian Inversion
• Modular invariant holographic correlators for $\mathcal{N}=4$ SYM with general gauge group
• 6d (2,0) and M-theory at 1-loop
• On Mellin Amplitudes in SCFTs with Eight Supercharges
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• More on holographic correlators: Twisted and dimensionally reduced structures
• Five-Dimensional Non-Lorentzian Conformal Field Theories and their Relation to Six-Dimensions
• ABJ Correlators with Weakly Broken Higher Spin Symmetry
• The type IIA Virasoro-Shapiro amplitude in AdS${}_4$ $\times$ CP${}^3$ from ABJM theory
• Recursion Relations for Anomalous Dimensions in the 6d $(2,0)$ Theory
• Holographic S-fold theories at one loop
• Bootstrapping AdS${}_2\times$ S${}^2$ hypermultiplets: hidden four-dimensional conformal symmetry