Analytic Discrete Self-Similar Solutions of Einstein-Klein-Gordon at Large D

Discretely self-similar solutions govern critical collapse and have been known only numerically since Choptuik's pioneering work. Using the large-D expansion, where D is the spacetime dimension, we construct an infinite family of analytic solutions of the Einstein-massless-Klein-Gordon equations. In this limit, the field equations simplify drastically, and the solutions are encoded in a single function of time. We characterize their structure and compare them with numerical critical solutions at finite D, identifying both universal features and effects specific to large D.