On Superconformal Four-Point Mellin Amplitudes in Dimension $d>2$

Abstract

We present a universal treatment for imposing superconformal constraints on Mellin amplitudes for $\mathrm{SCF}{\mathrm{T}}_{\mathrm{d}}$ with $3\le d\le 6$. This leads to a new technique to compute holographic correlators, which is similar but complementary to the ones introduced in [1,2]. We apply this technique to theories in various spacetime dimensions. In addition to reproducing known results, we obtain a simple expression for next-next-to-extremal four-point functions in $Ad{S}_7\times S^4$. We also use this machinery on $Ad{S}_4\times S^7$ and compute the first holographic one-half BPS four-point function. We extract the anomalous dimension of the R-symmetry singlet double-trace operator with the lowest conformal dimension and find agreement with the 3d $\mathcal{N}=8$ numerical bootstrap bound at large central charge.

34 pages, 1 figure; v2: minor changes, typos corrected; v3: published version

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• Double Copy Relation for AdS
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• The M-theory Archipelago
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• Defect CFT in the 6d (2,0) theory from M2 brane dynamics in AdS${}_7\times$S${}^4$
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• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• More on holographic correlators: Twisted and dimensionally reduced structures
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• Regge trajectories for the (2,0) theories
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• Mellin amplitudes for $Ad{S}_3\times S^3$
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• An Elliptic One-Loop Amplitude in Anti-de-Sitter Space
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