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Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory

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 k^2 t_8(tr F^2)^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 k^2 t_8(tr F^4) receives contributions from all L. We verified these statements 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 that suggest that supersymmetry forbids ultraviolet divergences in N=8 supergravity up to at least eight loops.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-00410003
Contributor : Vanhove Pierre Connect in order to contact the contributor
Submitted on : Saturday, August 15, 2009 - 8:34:01 AM
Last modification on : Monday, December 13, 2021 - 9:16:01 AM

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  • HAL Id : hal-00410003, version 1
  • ARXIV : 0908.1923

Citation

Nathan Berkovits, Michael B. Green, Jorge G. Russo, P. Vanhove. Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory. 2009. ⟨hal-00410003⟩

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