On non-planar ABJM anomalous dimensions from M2 branes in AdS4 × S7/ℤk

Abstract

Planar parts of conformal dimensions of primary operators in U_k(N) × U_−k(N) ABJM theory are controlled by integrability. Strong coupling asymptotics of planar dimensions of operators with large spins can be found from the energy of semiclassical strings in AdS₄ × CP³ but computing non-planar corrections requires understanding higher genus string corrections. As was pointed out in arXiv:2408.10070, there is an alternative way to find the non-planar corrections by quantizing M2 branes in AdS₄ × S⁷/ℤ_k which are wrapped around the 11d circle of radius 1/k = λ/N and generalize spinning strings in AdS₄ × CP³. Computing the 1-loop correction to the energy of M2 brane that corresponds to the long folded string with large spin S in AdS₄ allowed to obtain a prediction for the large λ limit of non-planar corrections to the cusp anomalous dimension. Similar predictions were found for non-planar dimensions of operators dual to M2 branes that generalize the “short” and “long” circular strings with two equal spins J₁ = J₂ in CP³. Here we consider two more non-trivial examples of 1-loop M2 brane computations that correspond to: (i) long folded string with large spin S in AdS₄ and orbital momentum J in CP³ whose energy determines the generalized cusp anomalous dimension, and (ii) circular string with spin S in AdS₄ and spin J in CP³. We find the leading terms of the expansion of the corresponding 1-loop M2 brane energies in 1/k. We also discuss similar semiclassical 1-loop M2 brane computation in flat 11d background and comment on possible relation to higher genus corrections to energies in 10d string theory.