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Supersymmetry and R-symmetry Ward identities relate on-shell amplitudes in a supersymmetric field theory.
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The hook rule formula for the dimension of the irreps of S U ( n ) SU(n) can be found in H. Georgi, Lie Algebras in Particle Physics (Perseus Books, Reading, MA, 1999). A diagrammatic proof was given in H. Elvang, P. Cvitanovic and A. D. Kennedy, “Diagrammatic Young Projection Operators for U(n),” J. Math. Phys. 46
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Z. Bern, J. J. Carrasco, L. J. Dixon, H. Johansson, D. A. Kosower and R. Roiban, “Three-Loop Superfiniteness of N=8 Supergravity,” Phys. Rev. Lett. 98
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N. Arkani-Hamed, “What is the Simplest QFT?,” talk given at the Paris Workshop Wonders of Gauge Theory and Supergravity
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M. Kiermaier and S. G. Naculich, “A super MHV vertex expansion for N=4 SYM theory,” JHEP 0905
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R. E. Kallosh, “Counterterms in extended supergravities,” Phys. Lett. B 99
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