On-shell superamplitudes in N < 4 SYM
Journal
Journal of High Energy Physics
Journal Volume
2011
Journal Issue
9
Date Issued
2011
Author(s)
Abstract
We present an on-shell formalism for superamplitudes of pure N < 4 super Yang-Mills theory. Two superfields, Ψ and Ψ†, 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 [Ψ, Ψ†>-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 briey 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 NKMHV 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. © SISSA 2011.
Type
journal article