Rational Cuntz states peak on the free disk algebra

We apply realization theory of noncommutative (NC) rational multipliers of the Fock space, or free Hardy space of square–summable power series in several noncommuting variables to the convex analysis of states on the Cuntz algebra. We show, in particular, that a large class of Cuntz states that arise as the “NC Clark measures” of isometric NC rational multipliers are peak states for Popescu's free disk algebra in the sense of Clouâtre and Thompson.