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

TL;DR

This paper introduces a universal method for applying superconformal constraints to Mellin amplitudes in various dimensions, enabling new calculations of holographic correlators and confirming known results with novel insights.

Contribution

It develops a new technique for superconformal constraints on Mellin amplitudes, applicable across dimensions 3 to 6, and computes previously unknown holographic four-point functions.

Findings

Derived a simple expression for next-next-to-extremal four-point functions in AdS7×S4.

Computed the first holographic one-half BPS four-point function in AdS4×S7.

Matched the anomalous dimension of a double-trace operator with 3d bootstrap bounds.

Abstract

We present a universal treatment for imposing superconformal constraints on Mellin amplitudes for $\mathrm{SCFT_d}$ with $3\leq d\leq 6$. 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 $AdS_7\times S^4$. We also use this machinery on $AdS_4\times S^7$ 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.