Renormalizing (φ3)6theory in curved space-time

The renormalization of ${\phi }^3$ theory in a six-dimensional conformally flat space-time is discussed at the two-loop level. The background-field method and the momentum-space representation of the Feynman propagator are used to calculate the ultraviolet divergences of the effective action. It is shown that (${\phi }^3$ ${)}_6$ theory is renormalizable in a conformally flat space-time at the two-loop level. The counterterms are given to the two-loop order. The next-to-leading-order term in the β function for the coupling constant of the R${\phi }^2$ term is then obtained.