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The hyperlinear profile of a group measures the growth rate of the dimensionof unitary approximations to the group. We construct a finitely-presented groupwhose hyperlinear profile is at least subexponential, i.e. at least$\exp(1/\epsilon^{k})$ for some $0 < k < 1$. We use this group to give anexample of a two-player non-local game requiring subexponential Hilbert spacedimension to play near-perfectly.

A group with at least subexponential hyperlinear profile