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On-shell superamplitudes in \( \mathcal{N} < 4 \) SYM. (English) Zbl 1301.81120

Summary: We present an on-shell formalism for superamplitudes of pure \( \mathcal{N} < 4 \) super Yang-Mills theory. Two superfields, {\(\Phi\)} and \(\Phi^{\dagger}\), are required to describe the two CPT conjugate supermultiplets. Simple truncation prescriptions allow us to derive explicit tree-level MHV and NMHV superamplitudes with \( \mathcal{N} \)-fold SUSY. Any \( \mathcal{N} = 0,1,2 \) tree superamplitudes have large-\(z\) falloffs under super-BCFW shifts, except under [{\(\Phi\)}, \({\Phi}^{\dagger}\)-shifts. We show that this ‘bad’ shift is responsible for the bubble contributions to 1-loop amplitudes in \( \mathcal{N} = 0,1,2 \) 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 \( \mathcal{N} = 1 \) SUSY Ward identities and a clear description of the connection between 6d superamplitudes and the 4d ones for both \( \mathcal{N} = 4 \) and \( \mathcal{N} = 2 \) SYM. We outline extensions to \( \mathcal{N} < 8 \) super-gravity.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
83E15 Kaluza-Klein and other higher-dimensional theories
83E50 Supergravity
81T18 Feynman diagrams

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