Effective potential and phase transitions induced by curvature in gauge theories in curved spacetime

By the direct solution of the renormalisation group equation the general expression for a one-loop effective potential of an arbitrary massless theory with the accuracy of linear curvature terms is obtained. The possibility of a first-order phase transition induced by a curvature in gauge theories is investigated. It is shown that in the theory of a scalar field interacting with quantum R 2 gravity the phase transition leads to the induced classical gravity.