Sum rules for interface Hamiltonians

We derive exact identities for a general class of interface Hamiltonians describing wetting transitions that relate force fluctuations to interface fluctuations and the surface tension. These sum rules are analogous to the Triezenberg, Zwanzig and Wertheim formulas for the surface tension derived using the theory of inhomogeneous fluids. Relations between these two approaches are discussed. Our sum rules are consistent with the scaling theory of wetting transitions.