On Mellin Amplitudes in SCFTs with Eight Supercharges

TL;DR

This paper extends Mellin space techniques to compute four-point functions in superconformal theories with eight supercharges, analyzing flavor current correlators in five- and six-dimensional theories at large N.

Contribution

It develops a method to analyze four-point functions in theories with fewer supercharges, specifically addressing the impact of reduced R-symmetry and flavor channels.

Findings

Four-point functions are determined by superconformal symmetry up to two free parameters.

The method is applied to Seiberg theories in five dimensions and E-string theory in six dimensions.

Results show the fixed structure of flavor current correlators at large N.

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 Poincar\'e 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.