Renormalization ofgφ3theory in a six-dimensional conformally flat space-time

Using dimensional regularization and 't Hooft's renormalization scheme, ${\phi }^3$ theory is renormalized at the one-loop level in a six-dimensional conformally flat space-time. The calculation is done by treating the scalar curvature as an interaction term. Using the renormalization group the effective conformal coupling $\xi \left(\kappa \right)$ is calculated and it is shown that in the UV limit $\xi \left(\kappa \right)\to \frac{6}{25}$ as $\kappa \to \infty$, instead of the conformal value of $\frac{1}{5}$.