Oscillating Multiple Giants

Abstract

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 $\mathcal{N}=4$ 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.

arXiv comment43 pages, v2: references added, v3: corrected the argument on the commutation relations and the central extension of su(2|2)

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