Abstract
The constraints imposed by maximal supersymmetry on multi-loop contributions to the scattering of four open superstrings in the U(N) theory are examined by use of the pure spinor formalism. The double-trace term k2 t8(tr F2)2 (where k represents an external momentum and F the Yang-Mills field strength) only receives contributions from L ⩽ 2 (where L is the loop number) while the single-trace term k2 t8(tr F4) receives contributions from all L. These statements are verified up to L = 5, but arguments based on supersymmetry suggest they extend to all L. This explains why the single-trace contributions to low energy maximally supersymmetric Yang-Mills field theory are more divergent in the ultraviolet than the double-trace contributions. We also comment further on the constraints on closed string amplitudes and their implications for ultraviolet divergences in = 8 supergravity.
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