The crumpling transition of membranes driven by quantum fluctuations in a D=epsilon expansion

We consider a D-dimensional fluid membrane in a D+1-dimensional embedding space, subject to quantum fluctuations. The corresponding action is invariant under coordinate transformations and depends only on the shape of the membrane and its variation, neglecting tangential degrees of freedom. We calculate the resulting field theory to one loop order in a D=epsilon expansion and find a quantum transition even at T=0.