  We discuss an effective field theory (EFT) approach to the computation of
fluctuation-induced interactions between particles bound to a thermally
fluctuating fluid surface controlled by surface tension. By describing
particles as points, EFT avoids computing functional integrals subject to
difficult constraints. Still, all information pertaining to particle size and
shape is systematically restored by amending the surface Hamiltonian with a
derivative expansion. The free energy is obtained as a cumulant expansion, for
which straightforward techniques exist. We derive a complete description for
rigid axisymmetric objects, which allows us to develop a full asymptotic
expansion in powers of the inverse distance for the pair interaction. We also
demonstrate by a few examples the efficiency with which multibody interactions
can be computed. Moreover, although the main advantage of the EFT approach lies
in explicit computation, we discuss how one can infer certain features of cases
involving flexible or anisotropic objects. The EFT description also permits a
systematic computation of ground-state surface-mediated interactions, which we
illustrate with a few examples.
