Free product von Neumann algebras associated to graphs, and Guionnet, Jones, Shlyakhtenko subfactors in infinite depth

Given a subfactor planar algebra PP, Guionnet, Jones and Shlyakhtenko give a diagrammatic construction of a II1II1 subfactor whose planar algebra is PP. They showed that if PP is finite-depth, then the factors are interpolated free group factors, and they identified the parameters. We prove that if PP is infinite-depth, then the factors are isomorphic to L(F∞)L(F∞).