Extremal couplings and gluon scattering in M-theory

TL;DR

This paper computes extremal cubic couplings in M-theory backgrounds with fixed points, uses them to analyze gluon correlators at strong coupling, and introduces a new reduced correlator solution for superconformal Ward identities.

Contribution

It provides explicit calculations of bulk couplings and correlators in M-theory duals with eight supercharges, and derives a universal reduced correlator solution for relevant CFTs.

Findings

Matching of graviton exchange with flat space limit

Explicit form of reduced correlator for superconformal Ward identities

Extension of results to all CFTs with eight supercharges in 3 to 6 dimensions

Abstract

We consider M-theory on the backgrounds AdS$_4\times S^7/\mathbb{Z}_{N_f}$ and AdS$_7\times S^4/\mathbb{Z}_2$, which have fixed point locii AdS$_{d+1}\times S^3$ for $d=3,6$. These theories are holographically dual to certain CFTs in $d=3,6$ with eight supercharges. We compute the bulk cubic couplings between graviton KK modes and gluon KK modes living on the fixed points of these theories, which are generically extremal. We use these couplings to compute the graviton exchange term that appears in the strong coupling expansion of holographic correlators of gluon KK modes $\langle 22pp\rangle$ in these theories, and check that it matches the expected flat space limit. We express the answer in terms of a new reduced correlator solution to the superconformal Ward identities, which we derive for all CFTs with eight supercharges in $3\leq d\leq6$.