Dynamical breakdown of symmetry in quadratic quantum gravity

In the ladder approximation, the effective potential for composite fermion fields and Schwinger-Dyson equations are explicitly obtained in R2 gravity against a flat background. The two-dimensional case is considered in the covariant and conformal gauges, while the four-dimensional case is treated in the covariant gauge, which ensures the absence of nonminimal terms in the graviton propagator. A detailed numerical analysis of nonlinear integral equations for structure functions that determine the exact fermion propagator is performed. The dynamical fermion mass is found as a function of the coupling constant. It is shown that, in all gauges considered in this study, there exists a phase transition accompanied by the breakdown of chiral symmetry and by the dynamical generation of a fermion mass