M-theory on AdS_4xM^{111}: the complete Osp(2|4)xSU(3)xSU(2) spectrum from harmonic analysis

TL;DR

This paper computes the complete spectrum of supergravity compactification on AdS_4xM^{111} using harmonic analysis, providing essential data for testing the AdS_4/CFT_3 correspondence in a specific N=2 setting.

Contribution

It offers the first full spectrum calculation for the AdS_4xM^{111} compactification, extending harmonic analysis techniques to this case and aiding in the validation of AdS/CFT correspondence.

Findings

Complete spectrum of long, short, and massless representations derived.

Provides a systematic scheme for other N=2 compactifications.

Facilitates detailed comparison between supergravity spectra and dual CFT operators.

Abstract

We reconsider the Kaluza Klein compactifications of D=11 supergravity on AdS_4x(G/H)_7 manifolds that were classified in the eighties, in the modern perspective of AdS_4/CFT_3 correspondence. We focus on one of the three N=2 cases: (G/H)_7=M^{111}=SU(3)xSU(2)xU(1)/SU(2)xU(1)'xU(1)''. Relying on the systematic use of the harmonic analysis techniques developed in the eighties by one of us (P. Fre') with R. D'Auria, we derive the complete spectrum of long, short and massless Osp(2|4)xSU(3)xSU(2) unitary irreducible representations obtained in this compactification. Our result also provides a general scheme for the other N=2 compactifications. Furthermore, it is a necessary comparison term in the AdS_4/CFT_3 correspondence: the complete AdS/CFT match of the spectra that we obtain will provide a much more stringent proof of the AdS/CFT correspondence than in the S^7 case, since the structure of the superconformal field theory on the M2-brane world volume must be such as to reproduce, at the level of composite operators, the flavor group representations, the conformal dimensions and the hypercharges that we obtain in the present article. The investigation of the match is left to future publications. Here we provide an exhaustive construction of the Kaluza Klein side of our spectroscopy.