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Report number	arXiv:1201.5366 ; CERN-PH-TH-2011-190 ; UCLA-11-TEP-110 ; SU-ITP-11-34 ; Saclay-IPhT-T11-175 ; SLAC-PUB-14529 ; NSF-KITP-11-236
Title	Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
Author(s)	Bern, Z (UCLA ; UC, Santa Barbara ; CERN) ; Carrasco, J J M (Stanford U., Phys. Dept. ; Stanford U., ITP ; UC, Santa Barbara) ; Dixon, L J (SLAC ; CERN) ; Johansson, H (Saclay, SPhT ; UC, Santa Barbara) ; Roiban, R (Penn State U. ; UC, Santa Barbara)
Publication	2012
Imprint	26 Jan 2012
Note	Comments: 61 pages, 22 figures
In:	Phys. Rev. D 85 (2012) 105014
DOI	10.1103/PhysRevD.85.105014
Subject category	Particle Physics - Theory
Abstract	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_c**2 single-trace divergence in N=4 super-Yang-Mills theory.
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