Abstract
We study the liberation process for projections: (p,q)↦(pt,q)=(utput⁎,q) where ut is a free unitary Brownian motion freely independent from {p,q}. Its action on the operator-valued angle qptq between the projections induces a flow on the corresponding spectral measures μt; we prove that the Cauchy transform of the measure satisfies a holomorphic PDE. We develop a theory of subordination for the boundary values of this PDE, and use it to show that the spectral measure μt possesses a piecewise analytic density for any t>0 and any initial projections of trace 12. We us this to prove the Unification Conjecture for free entropy and information in this trace 12 setting.
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