Oscillating Multiple Giants

We propose a new example of the AdS/CFT correspondence between the system of multiple giant gravitons in AdS${}_5 \times {}$S${}^5$ and the operators with $O(N_c)$ dimensions in ${\cal N}=4$ super Yang-Mills. We first extend the mixing of huge operators on the Gauss graph basis in the $su(2)$ sector to all loops of the 't Hooft coupling, by demanding the commutation of perturbative Hamiltonians in an effective $U(p)$ theory, where $p$ corresponds to the number of giant gravitons. The all-loop dispersion relation remains gapless at any $\lambda$, which suggests that harmonic oscillators of the effective $U(p)$ theory should correspond to the classical motion of the D3-brane that is continuously connected to non-maximal giant gravitons.