Simplifying Multi-loop Integrands of Gauge Theory and Gravity Amplitudes

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We use the duality between color and kinematics to simplify the construction of the complete four-loop four-point amplitude of N = 4 super-Yang-Mills theory, including the nonplanar contributions. The duality completely determines the amplitude's integrand in terms of just two planar graphs. The existence of a manifestly dual gauge-theory amplitude trivializes the construction of the corresponding N = 8 supergravity integrand, whose graph numerators are double copies (squares) of the N = 4 super-Yang-Mills numerators. The success of this procedure provides further nontrivial evidence that the duality and double-copy properties hold at loop level. The new form of the four-loop ... continued below

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61 pages

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Bern, Z.; Carrasco, J.J.M.; Dixon, L.J.; Johansson, H. & Roiban, R. February 15, 2012.

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We use the duality between color and kinematics to simplify the construction of the complete four-loop four-point amplitude of N = 4 super-Yang-Mills theory, including the nonplanar contributions. The duality completely determines the amplitude's integrand in terms of just two planar graphs. The existence of a manifestly dual gauge-theory amplitude trivializes the construction of the corresponding N = 8 supergravity integrand, whose graph numerators are double copies (squares) of the N = 4 super-Yang-Mills numerators. The success of this procedure provides further nontrivial evidence that the duality and double-copy properties hold at loop level. The new form of the four-loop four-point supergravity amplitude makes manifest the same ultraviolet power counting as the corresponding N = 4 super-Yang-Mills amplitude. We determine the amplitude's ultraviolet pole in the critical dimension of D = 11/2, the same dimension as for N = 4 super-Yang-Mills theory. Strikingly, exactly the same combination of vacuum integrals (after simplification) describes the ultraviolet divergence of N = 8 supergravity as the subleading-in-1/N{sub c}{sup 2} single-trace divergence in N = 4 super-Yang-Mills theory.

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61 pages

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  • Journal Name: Submitted to Physical Review D; Journal Volume: 85; Journal Issue: 10

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  • Report No.: SLAC-PUB-14529
  • Grant Number: AC02-76SF00515
  • DOI: 10.1103/PhysRevD.85.105014 | External Link
  • Office of Scientific & Technical Information Report Number: 1035115
  • Archival Resource Key: ark:/67531/metadc837585

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  • February 15, 2012

Added to The UNT Digital Library

  • May 19, 2016, 3:16 p.m.

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  • Dec. 1, 2016, 7:59 p.m.

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Bern, Z.; Carrasco, J.J.M.; Dixon, L.J.; Johansson, H. & Roiban, R. Simplifying Multi-loop Integrands of Gauge Theory and Gravity Amplitudes, article, February 15, 2012; United States. (digital.library.unt.edu/ark:/67531/metadc837585/: accessed May 25, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.