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

Abstract

$\mathrm{SU}(N)$ Coleman-Weinberg gauge theory is analyzed in the Einstein static universe (${R}^{1}\ifmmode\times\else\texttimes\fi{}{S}^{3}$). 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 ${{m}^{2}}_{\mathrm{eff}}=\frac{\ensuremath{-}3{g}^{2}N}{(16{\ensuremath{\pi}}^{2}{r}^{2})}$, 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.