Given a countably generated rigid C*-tensor category |${\sf C}$|, we construct a planar algebra P• whose category of projections |${\sf Pro}$| is equivalent to |${\sf C}$|. From P•, we use methods of Guionnet-Jones-Shlyakhtenko-Walker to construct a rigid C*-tensor category |${\sf Bim}$| whose objects are bifinite bimodules over an interpolated free group factor, and we show |${\sf Bim}$| is equivalent to |${\sf Pro}$|. We use these constructions to show |${\sf C}$| is equivalent to a category of bifinite bimodules over |$L(\mathbb {F}_\infty )$|.
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2012
American Institute of Physics
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