Abstract
The behavior of effective coupling constants in one-loop “finite” SU(2) gauge theories in curved space-time is investigated. It is shown that in strong gravitational field the effective coupling constants, corresponding to the parameters of non-minimal interaction of scalars and gravitational field, tend to the conformal values (asymptotical conformal invariance) or increase in an exponential fashion. The weak gravitational field limit is also considered in the same models.
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