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Abstract: Supersymmetry and R-symmetry Ward identities relate on-shell amplitudes in asupersymmetric field theory. We solve these Ward identities for Next-to^K MHVamplitudes of the maximally supersymmetric N=4 and N=8 theories. The resultingsuperamplitude is written in a new, manifestly supersymmetric and R-invariantform: it is expressed as a sum of very simple SUSY and SUN R-invariantGrassmann polynomials, each multiplied by a -basis amplitude-. For Next-to^KMHV n-point superamplitudes the number of basis amplitudes is equal to thedimension of the irreducible representation of SUn-4 corresponding to therectangular Young diagram with N columns and K rows. The linearly independentamplitudes in this algebraic basis may still be functionally related bypermutation of momenta. We show how cyclic and reflection symmetries can beused to obtain a smaller functional basis of color-ordered single-traceamplitudes in N=4 gauge theory. We also analyze the more significant reductionthat occurs in N=8 supergravity because gravity amplitudes are not ordered. Allresults are valid at both tree and loop level.

Autor: Henriette Elvang, Daniel Z. Freedman, Michael Kiermaier


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