Speaker
Description
In this talk, I will discuss recent progress toward understanding the spectrum of multi-trace operators in $\mathcal{N}=4$ SYM at large 't Hooft coupling and at tree level in the large-N expansion, focusing on triple-trace operators in the R-symmetry singlet sector. While partial information about these operators can be extracted from four-point functions, a complete understanding remains elusive, in part because of their large degeneracy at fixed spin. To extract the anomalous dimensions of these operators, we develop an AdS Hamiltonian approach, i.e., we diagonalize an effective Hamiltonian built from interactions involving the Lagrangian densities $L_p$, which are superdescendants of the stress-tensor superprimary and its Kaluza–Klein modes. We show that this Hamiltonian reproduces the known spectrum of double-trace operators and makes the hidden 10d symmetry manifest. We then compute its action on triple-trace operators built from three $L_p$'s, determining their anomalous dimensions as a function of spin. If time permits, I will also present preliminary results on higher-trace operators, exploring their eigenvalue statistics and possible signatures of chaotic behavior.