Prokopii Anempodistov (Paris): Study of protected BPS correlators of heavy operators in $\mathcal{N}=4$ SYM via complex matrix models and their holographic duals

We propose and study a family of complex matrix models computing the protected two- and three-point correlation functions in \mathcal{N}=4 SYM. Our description allows us to directly relate the eigenvalue density of the matrix model for “Huge“ operators with \Delta \sim N^2 to the shape of droplets in the dual Lin-Lunin-Maldacena (LLM) geometry. We demonstrate how to determine the eigenvalue distribution for various choices of operators such as those of exponential, character, or coherent state type, which then allows us to efficiently compute one-point functions of light chiral primaries in generic LLM backgrounds. We provide a large N formalism for one-point functions of “Giant“ probes, such as operators dual to giant graviton branes in LLM backgrounds, and explicitly apply it for particular backgrounds. We also explicitly compute the correlator of three huge half-BPS operators of exponential type and stacks of determinant operators by reducing them to the known matrix model problems such as the Potts or O(n) model on random planar graphs. Finally, we provide a proposal for holographic calculation of two- and three-point functions of “Huge“ and “Giant“ operators using Type IIB SUGRA, and find agreement with the large N limit of the gauge theory results.
The talk will be based on 2508.20094, 2603.28880 and two upcoming papers with Adolfo Holguin, Vladimir Kazakov, and Lev Senchukov.