Evanescent Effects can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences

Bern, Zvi; Cheung, Clifford; Chi, Huan-Hang; Davies, Scott; Dixon, Lance; Nohle, Josh

doi:10.1103/PhysRevLett.115.211301

Title: Evanescent Effects can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences

Journal Article · Tue Nov 17 00:00:00 EST 2015 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.115.211301· OSTI ID:1226183

Bern, Zvi; Cheung, Clifford; Chi, Huan-Hang; Davies, Scott; Dixon, Lance; Nohle, Josh

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) R³ 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. In addition, we concur and also find that the leading R³ 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.

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Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States); Univ. of California, Los Angeles, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); Gordon and Betty Moore Foundation (GBMF); National Science Foundation (NSF); Simons Foundation

Grant/Contract Number:: SC0009937; SC0010255; AC02-76SF00515; 776; 1066293

OSTI ID:: 1226183

Alternate ID(s):: OSTI ID: 1232660; OSTI ID: 1609082

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Vol. 115 Journal Issue: 21; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 55 works

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