Near-Extremal Correlators and Generalized Consistent Truncation for AdS_{4|7}\times S^{7|4}

TL;DR

The work investigates factorization and generalized consistent truncation for AdS/CFT in M-theory on ${\rm AdS}_4\times S^7$ and ${\rm AdS}_7\times S^4$, focusing on 1/2 BPS correlators in the dual $d=3$ ${\cal N}=8$ and $d=6$ $(0,2)$ SCFTs. By analyzing AdS integrals, it shows extremal correlators must factorize with vanishing extremal bulk couplings, consistent with finiteness of the bulk theory, and relates the overall normalization to 2- and 3-point data via OPE arguments. It then conjectures that near-extremal bulk couplings also vanish, leading to a decomposed, factorized structure for near-extremal correlators and a generalized truncation beyond standard KK reductions. This framework provides a coherent picture for correlator structure in strongly coupled 3d and 6d SCFTs and offers a path to extend non-renormalization-type insights from AdS5/CFT4 to M-theory contexts. The results have potential implications for hidden symmetries in gauged supergravity and for systematic truncations of KK towers in AdS/CFT with no marginal deformations.

Abstract

We present conjectures for the space-time form and leading large N dependence of extremal and near-extremal correlation functions in the \N=8 superconformal 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 $AdS_4\times §^7$ and $AdS_7 \times §^4$ respectively. As a key part of the conjectures, we argue that the bulk couplings associated with extremal and near-extremal field configurations in the corresponding $AdS_4$ and $AdS_7$ gauged supergravities vanish. The vanishing of these couplings constitutes a generalization of the property of consistent truncation of the Kaluza-Klein modes.