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

TL;DR

This paper revisits the S-matrix approach to the open superstring low energy effective Lagrangian, showing that fewer amplitudes are needed to determine higher-order terms due to supersymmetry constraints, at least up to order α'^4.

Contribution

It demonstrates that, unlike the bosonic case, supersymmetry constraints reduce the number of amplitudes needed to determine the effective Lagrangian terms, confirmed up to α'^4 order.

Findings

All bosonic terms up to α'^4 order can be derived from the 4-point amplitude.

Supersymmetry imposes kinematical constraints reducing amplitude requirements.

Results align with previous BPS configuration methods.

Abstract

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. By means of the KLT relations, our results can be mapped to the NS-NS sector of the low energy effective lagrangian of the type II string theories implying that there one can also find kinematical constraints in the $N$-point amplitudes and that important informations can be inferred, at least up to ${\alpha'}^4$ order, by only using the (tree level) 4-point amplitude.