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Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity

Michael B. Green·Jorge G. Russo·Pierre Vanhove
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Abstract

This paper considers general features of the derivative expansion of Feynman diagram contributions to the four-graviton scattering amplitude in eleven-dimensional supergravity compactified on a two-torus. These are translated into statements about interactions of the form D^2k R^4 in type II superstring theories, assuming the standard M-theory/string theory duality relationships, which provide powerful constraints on the effective interactions. In the ten-dimensional IIA limit we find that there can be no perturbative contributions beyond k string loops (for k>0). Furthermore, the genus h=k contributions are determined exactly by the one-loop eleven-dimensional supergravity amplitude for all values of k. A plausible interpretation of these observations is that the sum of h-loop Feynman diagrams of maximally extended supergravity is less divergent than might be expected and could be ultraviolet finite in dimensions d < 4 + 6/h -- the same bound as for N=4 Yang--Mills.

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Michael B. Green, Jorge G. Russo, Pierre Vanhove. 2007-02-28. Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity. https://doi.org/10.1088/1126-6708%2F2007%2F02%2F099

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