Revisiting the S-matrix approach to the open superstring low energy effective lagrangian

Understand

The conventional S-matrix approach to the (tree level) open string low energy effective lagrangian assumes that, in order to obtain all its bosonic ${\alpha'}^N$ order terms, it is necessary to know the open string (tree level) $(N+2)$-point amplitude of massless bosons, at least expanded at that order in $\alpha'$.

• In this work we clarify that the previous claim is indeed valid for the bosonic open string, but for the supersymmetric one the situation is much more better than that: there are constraints in the kinematical bosonic terms of the amplitude (probably due to Spacetime Supersymmetry) such that a much lower open superstring $n$-point amplitude is needed to find all the ${\alpha'}^N$ order terms.
• In this `revisited' S-matrix approach we have checked that, at least up to ${\alpha'}^4$ order, using these kinematical constraints and only the known open superstring 4-point amplitude, it is possible to determine all the bosonic terms of the low energy effective lagrangian.
• The sort of results that we obtain seem to agree completely with the ones achieved by the method of BPS configurations, proposed about ten years ago.