On Mellin Amplitudes in SCFTs with Eight Supercharges

TL;DR

The paper advances holographic computations of four-point functions for theories with eight Poincaré supercharges by adapting the Mellin-space framework to moment-map operators in the $D[2]$ multiplet, which transform in the adjoint of a flavor group. By formulating a constrained Mellin amplitude ansatz and enforcing Mellin-space superconformal Ward identities, the authors show that the flavor-current four-point functions are fixed up to two physical parameters, identified with the squared OPE coefficients of the stress tensor and flavor current multiplets (i.e., bulk gravitational and gauge couplings). They implement the method for Seiberg theories in five dimensions and the E-string theory in six dimensions, deriving explicit contact-term structures across multiple flavor representations for several groups ($E_1 o SU(2)$, $E_6$, $E_7$, $E_8$) and providing the corresponding $ ext{λ}_S$ and $ ext{λ}_F$ values from holography or independent data. In the E-string case the truncation yields rational exchange amplitudes, and the two-parameter data can be extracted and checked against bootstrap expectations, offering precise bulk-coupling data to connect holography with non-maximally supersymmetric SCFT dynamics.

Abstract

We extend the Mellin space techniques of [1] for computing holographic four-point correlation functions in maximally superconformal theories to theories with only eight Poincaré supercharges. The one-half BPS operators in these correlators are taken to be the superconformal primary in the $\mathcal{D}[k]$ multiplet (with $k=2$ corresponding to the flavor current multiplet), and transform in the adjoint representation of a flavor group $G$. Because of the smaller R-symmetry group $SU(2)$, each individual superconformal Ward identity is less powerful. On the other hand, the constraining power is compensated in number by the different flavor channels in the four-point function. As concrete test cases, we study the Seiberg theories in five dimensions and E-string theory in six dimensions at the large $N$ limit. We show that the flavor current multiplet four-point functions are fixed by superconformal symmetry up to two free parameters, which are proportional to the squared OPE coefficients for the flavor current multiplet and the stress tensor multiplet.