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

Bern, Zvi and Cheung, Clifford and Chi, Huan-Hang and Davies, Scott and Dixon, Lance and Nohle, Josh (2015) Evanescent Effects Can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences. Physical Review Letters, 115 (21). Art. No. 211301. ISSN 0031-9007.

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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.

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Additional Information:© 2015 Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Received 3 August 2015; published 17 November 2015. We especially thank David Kosower, Radu Roiban, Augusto Sagnotti and Raman Sundrum for many useful and interesting discussions and suggestions. We also thank Luis Alvarez-Gaume, John Joseph Carrasco, Stanley Deser, Paolo Di Vecchia, Gary Horowitz, Henrik Johansson, Tim Jones, Kelly Stelle and Mark Wise for helpful discussions. This material is based upon and supported by the Department of Energy under Award Number DE-SC0009937 and contract DE–AC02–76SF00515 and the Gordon and Betty Moore Foundation through Grant No. 776 to the Caltech Moore Center for Theoretical Cosmology and Physics. CC is supported by a DOE Early Career Award DE-SC0010255 and a Sloan Research Fellowship. ZB and LD are grateful to the Simons Foundation for support and to the Walter Burke Institute at Caltech for hospitality. CC and LD thank the Aspen Center for Physics and the NSF Grant #1066293 for hospitality. SD and JN gratefully acknowledge Mani Bhaumik for his generous support.
Group:Walter Burke Institute for Theoretical Physics, Moore Center for Theoretical Cosmology and Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0009937
Department of Energy (DOE)DE–AC02–76SF00515
Gordon and Betty Moore Foundation776
Department of Energy (DOE)DE-SC0010255
Simons FoundationUNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
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Issue or Number:21
Classification Code:PACS numbers: 04.65.+e, 11.15.Bt, 11.25.Db, 12.60.Jv
Record Number:CaltechAUTHORS:20150731-185747920
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:59130
Deposited By: Joy Painter
Deposited On:06 Aug 2015 18:37
Last Modified:03 Oct 2019 08:43

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