Dynamical mass generation inSU(N)Coleman-Weinberg gauge theory in the Einstein static universe

$\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ Coleman-Weinberg gauge theory is analyzed in the Einstein static universe ($R^1\times S^3$). Massless scalar fields in the adjoint representation with conformally invariant couplings to gravity acquire negative dynamical masses, ${m^2}_{\mathrm{eff}}$, due to gauge interactions. We find ${m^2}_{\mathrm{eff}}=\frac{-3\mathrm{}{g}^{2}N}{\left(16\mathrm{}{\pi }^2{r}^2\right)}$, where $g$ and $r$ are a gauge coupling constant and a radius of $S^3$, respectively. Renormalization problems are carefully handled by using zeta-function regularization. An effective potential is also given.