Problem of singular solutions for effective coupling constants in quantum R2 gravity with matter

The asymptotic behaviour of effective coupling constants in the unified theory, which includes the quantum R2 gravity and the gauge theory is based on the SU(N) group and including scalar and spinor multiplets is studied. Investigation of singular solutions of the renormalization group equations has shown that for the conformal version of the theory the quantum gravity can weaken the restraints on the structure of the theory imposed by the asymptotic freedom. At the same time, the general version of the R2 gravity excludes the existence of singular solutions of the renormalization group equations