N=4 SYM NMHV Loop Amplitude in Superspace

Here we construct N=4 SuperYang-Mills 6 point NMHV loop amplitude (amplitudes with three minus helicities) as a full superspace form, using the $SU(4{)}_R$ anti-commuting spinor variables. Amplitudes with different external particle and cyclic helicity ordering are then just a particular expansion of this fermionic variable. We’ve verified this by explicit expansion obtaining amplitudes with two gluino calculated before. We give results for all gluino $A({\mathrm{\Lambda }}^{-}{\mathrm{\Lambda }}^{-}{\mathrm{\Lambda }}^{-}{\mathrm{\Lambda }}^{+}{\mathrm{\Lambda }}^{+}{\mathrm{\Lambda }}^{+})$and all scalar $A(\varphi \varphi \varphi \varphi \varphi \varphi )$scattering amplitude. A discussion of using MHV vertex approach to obtain these amplitudes are given, which implies a simplification for general loop amplitudes.