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Title: Cancellations Beyond Finiteness in N=8 Supergravity at Three Loops

Abstract

We construct the three-loop four-point amplitude of N=8 supergravity using the unitarity method. The amplitude is ultraviolet finite in four dimensions. Novel cancellations, not predicted by traditional superspace power-counting arguments, render its degree of divergence in D dimensions no worse than that of N=4 super-Yang-Mills theory--a finite theory in four dimensions. Similar cancellations can be identified at all loop orders in certain unitarity cuts, suggesting that N=8 supergravity may be a perturbatively finite theory of quantum gravity.

Authors:
; ;  [1];  [2];  [3];  [4];  [5]
  1. Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1547 (United States)
  2. Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309 (United States)
  3. Service de Physique Theorique, CEA-Saclay, F-91191 Gif-sur-Yvette cedex (France)
  4. (Switzerland)
  5. Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802 (United States)
Publication Date:
OSTI Identifier:
20951248
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 16; Other Information: DOI: 10.1103/PhysRevLett.98.161303; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; QUANTUM GRAVITY; SUPERGRAVITY; ULTRAVIOLET RADIATION; UNITARITY; YANG-MILLS THEORY

Citation Formats

Bern, Z., Carrasco, J. J., Johansson, H., Dixon, L. J., Kosower, D. A., Institut fuer Theoretische Physik, Universitaet Zuerich, CH-8057 Zurich, and Roiban, R. Cancellations Beyond Finiteness in N=8 Supergravity at Three Loops. United States: N. p., 2007. Web. doi:10.1103/PHYSREVLETT.98.161303.
Bern, Z., Carrasco, J. J., Johansson, H., Dixon, L. J., Kosower, D. A., Institut fuer Theoretische Physik, Universitaet Zuerich, CH-8057 Zurich, & Roiban, R. Cancellations Beyond Finiteness in N=8 Supergravity at Three Loops. United States. doi:10.1103/PHYSREVLETT.98.161303.
Bern, Z., Carrasco, J. J., Johansson, H., Dixon, L. J., Kosower, D. A., Institut fuer Theoretische Physik, Universitaet Zuerich, CH-8057 Zurich, and Roiban, R. Fri . "Cancellations Beyond Finiteness in N=8 Supergravity at Three Loops". United States. doi:10.1103/PHYSREVLETT.98.161303.
@article{osti_20951248,
title = {Cancellations Beyond Finiteness in N=8 Supergravity at Three Loops},
author = {Bern, Z. and Carrasco, J. J. and Johansson, H. and Dixon, L. J. and Kosower, D. A. and Institut fuer Theoretische Physik, Universitaet Zuerich, CH-8057 Zurich and Roiban, R.},
abstractNote = {We construct the three-loop four-point amplitude of N=8 supergravity using the unitarity method. The amplitude is ultraviolet finite in four dimensions. Novel cancellations, not predicted by traditional superspace power-counting arguments, render its degree of divergence in D dimensions no worse than that of N=4 super-Yang-Mills theory--a finite theory in four dimensions. Similar cancellations can be identified at all loop orders in certain unitarity cuts, suggesting that N=8 supergravity may be a perturbatively finite theory of quantum gravity.},
doi = {10.1103/PHYSREVLETT.98.161303},
journal = {Physical Review Letters},
number = 16,
volume = 98,
place = {United States},
year = {Fri Apr 20 00:00:00 EDT 2007},
month = {Fri Apr 20 00:00:00 EDT 2007}
}
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  • We construct the three-loop four-point amplitude of N = 8 supergravity using the unitarity method. The amplitude is ultraviolet finite in four dimensions. Novel cancellations, not predicted by traditional superspace power-counting arguments, render its degree of divergence in D dimensions to be no worse than that of N = 4 super-Yang-Mills theory--a finite theory in four dimensions. Similar cancellations can be identified at all loop orders in certain unitarity cuts, suggesting that N = 8 supergravity may be a perturbatively finite theory of quantum gravity.
  • Using the method of maximal cuts, we obtain a form of the three-loop four-point scattering amplitude of N = 8 supergravity in which all ultraviolet cancellations are made manifest. The Feynman loop integrals that appear have a graphical representation with only cubic vertices, and numerator factors that are quadratic in the loop momenta, rather than quartic as in the previous form. This quadratic behavior reflects cancellations beyond those required for finiteness, and matches the quadratic behavior of the three-loop four-point scattering amplitude in N = 4 super-Yang-Mills theory. By direct integration we confirm that no additional cancellations remain in themore » N = 8 supergravity amplitude, thus demonstrating that the critical dimension in which the first ultraviolet divergence occurs at three loops is D{sub c} = 6. We also give the values of the three-loop divergences in D = 7, 9, 11. In addition, we present the explicitly color-dressed three-loop four-point amplitude of N = 4 super-Yang-Mills theory.« less