  Previous treatments of three-dimensional (3D) short-ranged wetting
transitions have missed an entropic or low temperature Casimir contribution to
the binding potential describing the interaction between the unbinding
interface and wall. This we determine by exactly deriving the interfacial model
for 3D wetting from a more microscopic Landau-Ginzburg-Wilson Hamiltonian. The
Casimir term changes the interpretation of fluctuation effects occurring at
wetting transitions so that, for example, mean-field predictions are no longer
obtained when interfacial fluctuations are ignored. While the Casimir
contribution does not alter the surface phase diagram, it significantly
increases the adsorption near a first-order wetting transition and changes
completely the predicted critical singularities of tricritical wetting,
including the non-universality occurring in 3D arising from interfacial
fluctuations. Using the numerical renormalization group we show that, for
critical wetting, the asymptotic regime is extremely narrow with the growth of
the parallel correlation length characterised by an effective exponent in
quantitative agreement with Ising model simulations, resolving a longstanding
controversy.
