Speaker
Description
Three point-correlation functions of half-BPS operators in 𝒩=4 SYM are deceivingly complex observables. Non-renormalization theorems tell us that they can be exactly computed at the free point of the theory making them a perfect target for understanding non-perturbative gravitational effects in the large N expansion in regimes where the planar expansion is inadequate.
I will review techniques to efficiently compute such correlators in cases where the dimensions of the participating operators scale with powers of N. These methods allow us to systematically reproduce one-point functions of light single trace in general half-BPS backgrounds of type IIB supergravity. For the inverse reconstruction problem, I will explain how to build explicit operators dual to arbitrary LLM geometries. Then I will demonstrate how to extend these results to compute novel one-point functions of heavy probes in the large N limit via a D-instanton type formula. This gives sharp predictions for exact holographic vev's of giant graviton branes in LLM backgrounds. I will then present some results for correlation function of three heavy (Δ~N^2) operators.
I will finally comment on extensions of these techniques beyond the half-BPS sector, and the possible relation of the correlation functions of 1/4 and 1/8 BPS to lattice reductions of gauge theories.
