Near-extremal correlators and generalized consistent truncation for AdS(4 vertical bar 7) x S-7 vertical bar 4

We present conjectures for the space-time form and leading large-N dependen ce of extremal and near-extremal correlation functions in the N = 8 superco nformal Yang-Mills theory in d = 3 as well as in the (0, 2) superconformal theory in d = 6, using their gravity duals with M-theory on AdS(4) x S-7 an d AdS(7) x S-4 respectively. As a key part of the conjectures, we argue tha t the bulk couplings associated with extremal and near-extremal field confi gurations in the corresponding AdS(4) and AdS(7) gauged supergravities vani sh. The vanishing of these couplings constitutes a generalization of the pr operty of consistent truncation of the Kaluza-Klein modes.