title: Evanescent Effects can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences.
abstract: Evanescent operators such as the Gauss-Bonnet term have vanishing perturbative matrix elements in exactly D=4 dimensions. Similarly, evanescent fields do not propagate in D=4; a three-form field is in this class, since it is dual to a cosmological-constant contribution. In this Letter, we show that evanescent operators and fields modify the leading ultraviolet divergence in pure gravity. To analyze the divergence, we compute the two-loop identical-helicity four-graviton amplitude and determine the coefficient of the associated (nonevanescent) R^{3} counterterm studied long ago by Goroff and Sagnotti. We compare two pairs of theories that are dual in D=4: gravity coupled to nothing or to three-form matter, and gravity coupled to zero-form or to two-form matter. Duff and van Nieuwenhuizen showed that, curiously, the one-loop trace anomaly-the coefficient of the Gauss-Bonnet operator-changes under p-form duality transformations. We concur and also find that the leading R^{3} divergence changes under duality transformations. Nevertheless, in both cases, the physical renormalized two-loop identical-helicity four-graviton amplitude can be chosen to respect duality. In particular, its renormalization-scale dependence is unaltered.
authors.affiliation: Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, California 90095, USA.|Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA.|Department of Physics, CERN Theory Division, CH-1211 Geneva 23, Switzerland.
authors.forename: Zvi
authors.initials: Z
authors.lastname: Bern
authors.affiliation: Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA.
authors.forename: Clifford
authors.initials: C
authors.lastname: Cheung
authors.affiliation: SLAC National Accelerator Laboratory, Stanford University, Stanford, California 94309, USA.
authors.forename: Huan-Hang
authors.initials: HH
authors.lastname: Chi
authors.affiliation: Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, California 90095, USA.
authors.forename: Scott
authors.initials: S
authors.lastname: Davies
authors.affiliation: Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA.|SLAC National Accelerator Laboratory, Stanford University, Stanford, California 94309, USA.
authors.forename: Lance
authors.initials: L
authors.lastname: Dixon
authors.affiliation: Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, California 90095, USA.
authors.forename: Josh
authors.initials: J
authors.lastname: Nohle