S-matrix approach to the superstring low energy effective revisited

Full text: Conventional wisdom about the S-matrix approach to the (tree level) open string low energy effective Lagrangian (OSLEEL) states that, in order to obtain all its α'n order terms, it is necessary to know the open string (tree level) (n + 2)-point amplitude of gauge bosons, at least expanded at that order Lagrangian α'. In this work we review our recent result which clarifies that this common wisdom is indeed valid for the bosonic string but that, in the case of the open superstring, the situation is much more better than that. Spacetime Supersymmetry imposes constraints on the bosonic terms of the OSLEEL in such a way that (presumably) only the 4-point amplitude is needed to compute the complete nonabelian OSLEEL. If this is true it also implies, via KLT relations, that the closed superstring 4-point amplitude and Supersymmetry are enough to obtain completely the NS-NS sector of the (tree level) low energy effective action of the type II string theories. We apply this 'revisited' S-matrix approach to find the bosonic terms of the OSLEEL up to α'4 order terms. Our result is in perfect agreement with the 4 and 5-point amplitudes at that α' order and it also reproduces correctly the abelian limit of the F6 terms. This seems to agree completely with the previously known result obtained by the method of BPS configurations. (author)