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Title: Evanescent effects can alter ultraviolet divergences in quantum gravity without physical consequences

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.
Authors:
 [1] ;  [2] ;  [3] ;  [4] ;  [5] ;  [4]
  1. Univ. of California at Los Angeles, Los Angeles, CA (United States); California Institute of Technology, Pasadena, CA (United States); CERN Theory Division, Geneva (Switzerland)
  2. California Institute of Technology, Pasadena, CA (United States)
  3. SLAC National Accelerator Lab., Menlo Park, CA (United States)
  4. Univ. of California at Los Angeles, Los Angeles, CA (United States)
  5. California Institute of Technology, Pasadena, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
Publication Date:
Grant/Contract Number:
SC0009937; SC0010255; AC02-76SF00515; 776; 1066293
Type:
Published Article
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 115; Journal Issue: 21; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Research Org:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
OSTI Identifier:
1226183
Alternate Identifier(s):
OSTI ID: 1232660