Interacting scalar field theory in general curved space-time

The ultraviolet divergences of two-loop diagrams in general curved space-time are determined for the six-dimensional ${\phi }^3$ theory. The background-field method is used to evaluate the effective action. In order to isolate the short-distance singularities, the Feynman propagator is expanded by the heat kernel and dimensional regularization is employed. The gravitational counterterms as well as those for the matter field are explicitly given to the two-loop order.