  The hyperlinear profile of a group measures the growth rate of the dimension
of unitary approximations to the group. We construct a finitely-presented group
whose 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 an
example of a two-player non-local game requiring subexponential Hilbert space
dimension to play near-perfectly.
