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Curvature and topological effects on dynamical symmetry breaking in a four- and eight-fermion interaction model

A dynamical mechanism for symmetry breaking is investigated under the circumstances with the finite curvature, finite size and non-trivial topology. A four- and eight-fermion interaction model is considered as a prototype model which induces symmetry breaking at GUT era. Evaluating the effective potential in the leading order of the 1/N-expansion by using the dimensional regularization, we explicitly calculate the phase boundary which divides the symmetric and the broken phase in a weakly curved space-time and a flat space-time with non-trivial topology, $R^{D-1} \otimes S^1$.