Holographic Four-Point Functions in the (2, 0) Theory

Abstract

We revisit the calculation of holographic correlators for eleven-dimensional supergravity on $Ad{S}_7\times S^4$. Our methods rely entirely on symmetry and eschew detailed knowledge of the supergravity effective action. By an extension of the position space approach developed in [1, 2] for the $Ad{S}_5\times S^5$ background, we compute four-point correlators of one-half BPS operators for identical weights $k=2,3,4$. The $k=2$ case corresponds to the four-point function of the stress-tensor multiplet, which was already known, while the other two cases are new. We also translate the problem in Mellin space, where the solution of the superconformal Ward identity takes a surprisingly simple form. We formulate an algebraic problem, whose (conjecturally unique) solution corresponds to the general one-half BPS four-point function.

33 pages; v2: typos corrected, to appear on JHEP

References in corpus (9)

• Writing CFT correlation functions as AdS scattering amplitudes
• Spinning AdS Propagators
• Mellin amplitudes for $Ad{S}_5\times S^5$
• Conformal Bootstrap in Mellin Space
• Loop Corrections to Supergravity on $Ad{S}_5\times S^5$
• Loop corrections for Kaluza-Klein AdS amplitudes
• Four-point correlators with higher weight superconformal primaries in the AdS/CFT Correspondence
• Towards a Bootstrap approach to higher orders of epsilon expansion
• Exploring Perturbative Conformal Field Theory in Mellin space

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• $\mathbf{Ad}{\mathbf{S}}_3\times {\mathbf{S}}^3$ Tree-Level Correlators: Hidden Six-Dimensional Conformal Symmetry
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• The M-Theory S-Matrix From ABJM: Beyond 11D Supergravity
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• M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture
• Defect CFT in the 6d (2,0) theory from M2 brane dynamics in AdS${}_7\times$S${}^4$
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• Five-Dimensional Path Integrals for Six-Dimensional Conformal Field Theories
• Bootstrapping AdS${}_2\times$ S${}^2$ hypermultiplets: hidden four-dimensional conformal symmetry
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• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories
• Rebooting quarter-BPS operators in $\mathcal{N}=4$ Super Yang-Mills