Membranes from monopole operators in ABJM theory: Large angular momentum and M-theoretic AdS4/CFT3

Abstract

We study the duality between M-theory in AdS-4 \times S7/\mathbb {Z}-k and the ABJM \mathcal {N}=6 Chern-Simons-matter theory with gauge group U(N) \times \hbox {U}(N) and level k, taking N large and k of order 1. In this M-theoretic regime the lack of an explicit formulation of M-theory in AdS-4 \times S7/\mathbb {Z}-k makes the gravity side difficult, while the CFT is strongly coupled and the planar approximation is not applicable. We focus on states on the gravity side with large angular momentum J\gg 1 associated with a single plane of rotation in S7 and identify their dual operators in the CFT. We show that natural approximation schemes arise on both sides thanks to the presence of the small parameter 1/J. On the AdS side, we use the matrix model of M-theory on the maximally supersymmetric pp-wave background with matrices of size J/k. A perturbative treatment of this matrix model provides a good approximation to M-theory in AdS-4 \times S7/\mathbb {Z}-k when N{1/3}\ll J\ll N{1/2}. On the CFT side, we study the theory on S2\times \mathbb {R} with magnetic flux J/k. A Born-Oppenheimer-type expansion arises naturally for large J in spite of the theory being strongly coupled. The energy spectra on the two sides agree at leading order. This provides a non-trivial test of the AdS-4/CFT-3 correspondence including near-BPS observables associated with membrane degrees of freedom, thus verifying the duality beyond the previously studied sectors corresponding to either BPS observables or the type IIA string regime.