Heavy operators in superconformal Chern-Simons theory

We study the anomalous dimensions for scalar operators in Aharony-Bergman-Jafferis-Maldacena theory in the $SU(2)$ sector. The operators we consider have a classical dimension that grows as $N$ in the large $N$ limit. Consequently, the large $N$ limit is not captured by summing planar diagrams—nonplanar contributions have to be included. We find that the mixing matrix at two-loop order is diagonalized using a double coset ansatz, reducing it to the Hamiltonian of a set of decoupled oscillators. The spectrum of anomalous dimensions, when interpreted in the dual gravity theory, shows that the energy of the fluctuations of the corresponding giant graviton is dependent on the size of the giant. The first subleading corrections to the large $N$ limit are also considered. These subleading corrections to the dilatation operator do not commute with the leading terms, indicating that integrability may not survive beyond the large $N$ limit.