Fluctuation pressure of a fluid membrane between walls through six loops.

The fluctuation pressure that an infinitely extended fluid membrane exerts on two enclosing parallel hard walls is computed. Variational perturbation theory is used to extract the hard-wall limit from a perturbative expansion through six loops obtained with a smooth wall potential. Our result alpha=0.0821 +/- 0.0005 for the constant conventionally parametrizing the pressure lies above earlier Monte Carlo results.