The full Quantum Spectral Curve for AdS4/CFT3

Abstract The spectrum of planar N $$ \mathcal{N} $$ = 6 superconformal Chern-Simons theory, dual to type IIA superstring theory on AdS4 × CP 3, is accessible at finite coupling using integrability. Starting from the results of [ arXiv:1403.1859 ], we study in depth the basic integrability structure underlying the spectral problem, the Quantum Spectral Curve. The new results presented in this paper open the way to the quantitative study of the spectrum for arbitrary operators at finite coupling. Besides, we show that the Quantum Spectral Curve is embedded into a novel kind of Q-system, which reflects the OSp(4|6) symmetry of the theory and leads to exact Bethe Ansatz equations. The discovery of this algebraic structure, more intricate than the one appearing in the AdS5/CFT4 case, could be a first step towards the extension of the method to AdS3/CFT2.