Extremal correlators and random matrix theory

We study the correlation functions of Coulomb branch operators four-dimensional $\mathcal{N} = 2$ Superconformal Field Theories (SCFTs). focus on rank-one theories, such as SU(2) gauge theory with four fundamental hypermultiplets. "Extremal" functions, involving exactly one anti-chiral operator, are perhaps simplest nontrivial in Quantum Theory. show that large charge limit extremal correlators is captured by a "dual" description which chiral random matrix model Wishart-Laguerre type. This gives an analytic handle physics some particular excited states. In matrices we find non-relativistic axion-dilaton effective theory. The also admits 't Hooft expansion taken to be and simultaneously coupling zero. explains why obey double scaling states charge. give exact solution for first two orders compare expectations from field theory, previous weak results, analyze non-perturbative terms strong limit. Finally, apply techniques rank-1 Argyres-Douglas theories. our results available numerical bootstrap bounds.