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Infrared finite observables in N = 8 supergravity

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Abstract

Using the algorithm of constructing the IR finite observables discussed in detail in our earlier papers, we study the construction of such observables in N = 8 supergravity in the first nontrivial order of perturbation theory. In general, contrary to the amplitudes defined in the presence of some IR regulator, such observables do not reveal any “simple” structure.

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References

  1. L. J. Dixon, “Gluon Scattering in N = 4 Super-Yang-Mills Theory from Weak to Strong Coupling,” Proc. Sci. RADCOR2007, 056 (2007); arXiv: 0803.2475 [hep-th].

    Google Scholar 

  2. Z. Bern, L. Dixon, D. C. Dunbar, and D. A. Kosower, “Fusing Gauge Theory Tree Amplitudes into Loop Amplitudes,” Nucl. Phys. B 435, 59–101 (1995); arXiv: hep-ph/9409265.

    Article  Google Scholar 

  3. Z. Bern, L. Dixon, D. C. Dunbar, and D. A. Kosower, “One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits,” Nucl. Phys. B 425, 217–260 (1994); arXiv: hep-ph/9403226.

    Article  MathSciNet  MATH  Google Scholar 

  4. Z. Bern, M. Czakon, L. J. Dixon, D. A. Kosower, and V. A. Smirnov, “Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory,” Phys. Rev. D 75, 085010 (2007); arXiv: hep-th/0610248.

    Article  MathSciNet  Google Scholar 

  5. F. Cachazo, M. Spradlin, and A. Volovich, “Four-Loop Cusp Anomalous Dimension from Obstructions,” Phys. Rev. D 75, 105011 (2007); arXiv: hep-th/0612309.

    Article  MathSciNet  Google Scholar 

  6. D. C. Dunbar and P. S. Norridge, “Infinities within Graviton Scattering Amplitudes,” Class. Quantum Grav. 14, 351–365 (1997); arXiv: hep-th/9512084.

    Article  MathSciNet  MATH  Google Scholar 

  7. Z. Bern, L. Dixon, M. Perelstein, and J. S. Rozowsky, “Multi-leg One-Loop Gravity Amplitudes from Gauge Theory,” Nucl. Phys. B 546, 423–479 (1999); arXiv: hep-th/9811140.

    Article  MathSciNet  MATH  Google Scholar 

  8. Z. Bern, L. Dixon, D. C. Dunbar, M. Perelstein, and J. S. Rozowsky, “On the Relationship between Yang-Mills Theory and Gravity and Its Implication for Ultraviolet Divergences,” Nucl. Phys. B 530, 401–456 (1998); arXiv: hep-th/9802162.

    Article  Google Scholar 

  9. Z. Bern, J. J. Carrasco, L. J. Dixon, H. Johansson, D. A. Kosower, and R. Roiban, “Cancellations beyond Finiteness in N = 8 Supergravity at Three Loops,” Phys. Rev. Lett. 98, 161303 (2007); arXiv: hep-th/0702112.

    Article  Google Scholar 

  10. Z. Bern, J. J. M. Carrasco, L. J. Dixon, H. Johansson, and R. Roiban, “Ultraviolet Behavior of N = 8 Supergravity at Four Loops,” Phys. Rev. Lett. 103, 081301 (2009); arXiv: 0905.2326 [hep-th].

    Article  Google Scholar 

  11. Z. Bern, L. J. Dixon, and R. Roiban, “Is N = 8 Supergravity Ultraviolet Finite?,” Phys. Lett. B 644, 265–271 (2007); arXiv: hep-th/0611086.

    Article  MathSciNet  Google Scholar 

  12. N. Berkovits, “New Higher-Derivative R 4 Theorems for Graviton Scattering,” Phys. Rev. Lett. 98, 211601 (2007); arXiv: hep-th/0609006.

    Article  MathSciNet  Google Scholar 

  13. M. B. Green, J. G. Russo, and P. Vanhove, “Ultraviolet Properties of Maximal Supergravity,” Phys. Rev. Lett. 98, 131602 (2007); arXiv: hep-th/0611273.

    Article  Google Scholar 

  14. G. Bossard, P. S. Howe, and K. S. Stelle, “A Note on the UV Behaviour of Maximally Supersymmetric Yang-Mills Theories,” Phys. Lett. B 682, 137–142 (2009); arXiv: 0908.3883 [hep-th].

    Article  MathSciNet  Google Scholar 

  15. M. B. Green, J. G. Russo, and P. Vanhove, “String Theory Dualities and Supergravity Divergences,” J. High Energy Phys., No. 6, 075 (2010); arXiv: 1002.3805 [hep-th].

  16. L. Brink, S.-S. Kim, and P. Ramond, “E 7(7) on the Light Cone,” J. High Energy Phys., No. 6, 034 (2008); AIP Conf. Proc. 1078, 447–450 (2008); arXiv: 0801.2993 [hep-th].

  17. R. Kallosh and M. Soroush, “Explicit Action of E 7(7) on N = 8 Supergravity Fields,” Nucl. Phys. B 801, 25–44 (2008); arXiv: 0802.4106 [hep-th].

    Article  MathSciNet  Google Scholar 

  18. R. Kallosh and T. Kugo, “The Footprint of E 7(7) in Amplitudes of N = 8 Supergravity,” J. High Energy Phys., No. 1, 072 (2009); arXiv: 0811.3414 [hep-th].

  19. Z. Bern, J. J. M. Carrasco, and H. Johansson, “Progress on Ultraviolet Finiteness of Supergravity,” arXiv: 0902.3765 [hep-th].

  20. P. Vanhove, “The Critical Ultraviolet Behaviour of N = 8 Supergravity Amplitudes,” arXiv: 1004.1392 [hep-th].

  21. N. Arkani-Hamed, F. Cachazo, and J. Kaplan, “What Is the Simplest Quantum Field Theory?,” arXiv: 0808.1446 [hep-th].

  22. L. V. Bork, D. I. Kazakov, G. S. Vartanov, and A. V. Zhiboedov, “Infrared Safe Observables in N = 4 Super Yang-Mills Theory,” Phys. Lett. B 681, 296–303 (2009); arXiv: 0908.0387 [hep-th].

    Article  MathSciNet  Google Scholar 

  23. L. V. Bork, D. I. Kazakov, G. S. Vartanov, and A. V. Zhiboedov, “Construction of Infrared Finite Observables in N = 4 Super Yang-Mills Theory,” Phys. Rev. D 81, 105028 (2010); arXiv: 0911.1617 [hep-th].

    Article  Google Scholar 

  24. Z. Bern, L. J. Dixon, and V. A. Smirnov, “Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond,” Phys. Rev. D 72, 085001 (2005); arXiv: hep-th/0505205.

    Article  MathSciNet  Google Scholar 

  25. V. Del Duca, C. Duhr, and V. A. Smirnov, “An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM,” J. High Energy Phys., No. 3, 099 (2010); arXiv: 0911.5332 [hep-ph].

  26. V. Del Duca, C. Duhr, and V. A. Smirnov, “The Two-Loop Hexagon Wilson Loop in N = 4 SYM,” arXiv: 1003.1702 [hep-th].

  27. S. D. Ellis, Z. Kunszt, and D. E. Soper, “One-Jet Inclusive Cross Section at Order α 3s : Gluons Only,” Phys. Rev. D 40, 2188–2222 (1989).

    Article  Google Scholar 

  28. S. D. Ellis, Z. Kunszt, and D. E. Soper, “One-Jet Inclusive Cross Section at Order α 3s : Quarks and Gluons,” Phys. Rev. Lett. 64, 2121–2124 (1990).

    Article  Google Scholar 

  29. Z. Kunszt and D. E. Soper, “Calculation of Jet Cross Sections in Hadron Collisions at Order α 3s ,” Phys. Rev. D 46, 192–221 (1992).

    Article  Google Scholar 

  30. S. Frixione, Z. Kunszt, and A. Signer, “Three-Jet Cross Sections to Next-to-Leading Order,” Nucl. Phys. B 467, 399–442 (1996); arXiv: hep-ph/9512328.

    Article  Google Scholar 

  31. S. Catani and M. H. Seymour, “A General Algorithm for Calculating Jet Cross Sections in NLO QCD,” Nucl. Phys. B 485, 291–419 (1997); arXiv: hep-ph/9605323.

    Article  Google Scholar 

  32. T. Kinoshita, “Mass Singularities of Feynman Amplitudes,” J. Math. Phys. 3, 650–677 (1962).

    Article  MATH  Google Scholar 

  33. T. D. Lee and M. Nauenberg, “Degenerate Systems and Mass Singularities,” Phys. Rev. 133, B1549–B1562 (1964).

    Article  MathSciNet  Google Scholar 

  34. L. Dixon, “Calculating Scattering Amplitudes Efficiently,” arXiv: hep-ph/9601359.

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Correspondence to L. V. Bork.

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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Vol. 272, pp. 46–53.

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Bork, L.V., Kazakov, D.I., Vartanov, G.S. et al. Infrared finite observables in N = 8 supergravity. Proc. Steklov Inst. Math. 272, 39–46 (2011). https://doi.org/10.1134/S0081543811010056

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