On-shell superamplitudes in N<4 SYM

Abstract

We present an on-shell formalism for superamplitudes of pure N<4 super Yang-Mills theory. Two superfields, Phi and Phi^+, are required to describe the two CPT conjugate supermultiplets. Simple truncation prescriptions allow us to derive explicit tree-level MHV and NMHV superamplitudes with N-fold SUSY. Any N=0,1,2 tree superamplitudes have large-z falloffs under super-BCFW shifts, except under [Phi,Phi^+>-shifts. We show that this `bad' shift is responsible for the bubble contributions to 1-loop amplitudes in N=0,1,2 SYM. We evaluate the MHV bubble coefficients in a manifestly supersymmetric form and demonstrate for the case of four external particles that the sum of bubble coefficients is equal to minus the tree superamplitude times the 1-loop beta-function coefficient. The connection to the beta-function is expected since only bubble integrals capture UV divergences; we discuss briefly how the minus sign arises from UV and IR divergences in dimensional regularization. Other applications of the on-shell formalism include a solution to the N^{K}MHV N=1 SUSY Ward identities and a clear description of the connection between 6d superamplitudes and the 4d ones for both N=4 and N=2 SYM. We outline extensions to N<8 supergravity.

37 pages, 4 figures

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• Massive Supermultiplets in Four-Dimensional Superstring Theory
• On-shell diagrams and the geometry of planar N < 4 SYM theories
• Integrands for QCD rational terms and N=4 SYM from massive CSW rules
• One-loop renormalization and the S-matrix
• Gravitons, Bose-symmetry, and Bonus-scaling
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• All one-loop NMHV gluon amplitudes in N=1 SYM
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• Bilocal phase operators in beta-deformed super Yang-Mills