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The finite local conformally non-invariant $R^2$-term emerges in the one-loopeffective action of the model of quantum gravity based on the Weyl-squaredclassical action. This term is related to the $\Box R$ contribution to theconformal anomaly, which in a wide class of regularization schemes isdetermined by the second Schwinger-DeWitt (or Gilkey-Seeley) coefficient of theheat kernel expansion for inverse propagators of the theory. The calculation ofthis term requires evaluating the contributions of the fourth-order derivativeminimal and of the second-order nonminimal operators in the tensor and vectorsectors of the theory, corresponding to metric, ghost and gauge-fixingoperators. To ensure the correctness of existing formulas, we derived (andconfirmed) the result using a special technique of calculations, based on theheat-kernel representation of the Euclidean Green's function and the method ofuniversal functional traces.

On the local term in the anomaly-induced action of Weyl quantum gravity