Pseudo-Goldstone bosons in curved space-time

We calculate the effective potential for pseudo-Goldstone bosons (PGB's) in a toy SU(3) gauge theory broken by scalars in the adjoint representation, in a time indpendent curved space time with constant scalar curvature R. In both the strong and weak gravitational field limits, the effective potential for the PGB's picks up curvature dependent quadratic terms in one-loop order. Curiously, in the weak field limit, the gravitational contribution to the PGB mass is of the form RlogR, while in the opposite case (strong field) the expected form linear in R is recovered. A subtlety involved in determining the coupling of Goldstone bosons to the scalar curvature in theories with spontaneous symmetry breaking is described. 22 refs., 2 figs