Transchromatic phenomena in the equivariant slice spectral sequence

In this paper, we prove a transchromatic phenomenon for Hill--Hopkins--Ravenel and Lubin--Tate theories. This establishes a direct relationship between the equivariant slice spectral sequences of height-h and height-$(h/2)$ theories. As applications of this transchromatic phenomenon, we prove periodicity and vanishing line results for these theories.