For rational gluon amplitudes (one-loop all-plus and tree-level MHV), all (n-1)!/2 color-ordered partial amplitudes are determined by just two independent functions via polynomial syzygies.
String-Based Methods in Perturbative Gravity
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String theory implies a relatively modest growth in computational complexity for perturbative gravity calculations as compared to gauge theory calculations, contrary to field theory expectations. An explicit string-based calculation, which would be extremely difficult using conventional techniques, is presented to illustrate this.
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Serendipitous Syzygies of Scattering Amplitudes
For rational gluon amplitudes (one-loop all-plus and tree-level MHV), all (n-1)!/2 color-ordered partial amplitudes are determined by just two independent functions via polynomial syzygies.