Schwinger-DeWitt technique for quantum effective action in brane induced gravity models

We develop the Schwinger-DeWitt technique for the covariant curvature expansion of the quantum effective action for brane induced gravity models in curved spacetime. This expansion has a part nonanalytic in Dvali-Gabadadze-Porrati type scale parameter m, leading to the cutoff scale which is given by the geometric average of the mass of the quantum field in the bulk M and m. This cutoff M-cutoff = root Mm is much higher than the analogous strong coupling scale of the Dvali-Gabadadze-Porrati model treated by weak field expansion in the tree-level approximation. The lowest orders of this curvature expansion are calculated for the case of the scalar field in the (d + 1)-dimensional bulk with the brane carrying the d-dimensional kinetic term of this field. The ultraviolet divergences in this model are obtained for a particular case of d = 4.