Conformal dilaton gravity: Classical noninvariance gives rise to quantum invariance.

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When quantizing conformal dilaton gravity, there is a conformal anomaly which starts at two-loop order. This anomaly stems from evanescent operators on the divergent parts of the effective action. The general form of the finite counterterm, which is necessary in order to insure cancellation of the Weyl anomaly to every order in perturbation theory, has been determined using only conformal invariance. Those finite counterterms do not have any inverse power of any mass scale in front of them (precisely because of conformal invariance), and then they are not negligible in the low-energy deep infrared limit. The general form of the ensuing modifications to the scalar field equation of motion has been determined, and some physical consequences have been extracted.
©2016 American Physical Society. We are grateful for helpful discussions with Manuel Asorey and Mario Herrero-Valea. We also acknowledge a useful email exchange with Michael Duff as well as discussions with Roman Jackiw and So Young Pi. Part of this work was done while E. A. was at the Aspen Institute of Physics and at the Lawrence Berkeley Laboratory. We have been partially supported by the European Union FP7 ITN INVISIBLES (Marie Curie Actions, Grants No. PITN-GA-2011-289442 and No. HPRN-CT-200-00148 as well as by Grant No. FPA2012-31880 (Spain), Grant No. FPA2014- 54154-P, COST action MP1405 (Quantum Structure of Spacetime), and Grant No. S2009ESP-1473 (CA Madrid). The authors acknowledge the support of the Spanish MINECO Centro de Excelencia Severo Ochoa Programme under Grant No. SEV-2012-0249.
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