The crumpling transition of membranes driven by quantum fluctuations in a \(D=\varepsilon\) expansion (Q2767209)

A \(D\)-dimensional fluid membrane in a \((D + 1)\)-dimensional embedding space, subject to quantum fluctuations is considered. 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. The resulting field theory to one loop order in a \(D =\varepsilon \) expansion is presented, and a quantum transition at \(T = 0\) is found.