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

Luiz Antonio Barreiro, Ricardo Medina

TL;DR

The paper revisits the S-matrix program for the open superstring, showing that spacetime supersymmetry imposes a constraint that eliminates the need for high-point amplitudes to determine the bosonic part of the low-energy effective action. By exploiting the absence of $(\zeta\cdot k)^N$ terms in N-point amplitudes, the authors reduce the number of independent coefficients and determine the OSLEEL terms up to ${\alpha'}^4$ using mainly the 4-point amplitude, with results consistent with BPS-based methods. They explicitly derive the OSLEEL up to ${\alpha'}^3$ and, remarkably, obtain the full ${\alpha'}^4$ bosonic sector, including nontrivial tensor structures, in a non-perturbative way with respect to higher-point amplitudes. The approach hints at a deep link between open string amplitudes and the NS-NS sector of type II theories via KLT, suggesting a path to fully determine the closed-string low-energy action from tree-level data.

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 ${α'}^N$ 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 $α'$. 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 ${α'}^N$ order terms. In this `revisited' S-matrix approach we have checked that, at least up to ${α'}^4$ 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 ${α'}^4$ order, by only using the (tree level) 4-point amplitude.

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

TL;DR

The paper revisits the S-matrix program for the open superstring, showing that spacetime supersymmetry imposes a constraint that eliminates the need for high-point amplitudes to determine the bosonic part of the low-energy effective action. By exploiting the absence of terms in N-point amplitudes, the authors reduce the number of independent coefficients and determine the OSLEEL terms up to using mainly the 4-point amplitude, with results consistent with BPS-based methods. They explicitly derive the OSLEEL up to and, remarkably, obtain the full bosonic sector, including nontrivial tensor structures, in a non-perturbative way with respect to higher-point amplitudes. The approach hints at a deep link between open string amplitudes and the NS-NS sector of type II theories via KLT, suggesting a path to fully determine the closed-string low-energy action from tree-level data.

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 order terms, it is necessary to know the open string (tree level) -point amplitude of massless bosons, at least expanded at that order in . 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 -point amplitude is needed to find all the order terms. In this `revisited' S-matrix approach we have checked that, at least up to 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 -point amplitudes and that important informations can be inferred, at least up to order, by only using the (tree level) 4-point amplitude.

Paper Structure

This paper contains 33 sections, 79 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Brief review of gauge boson scattering amplitudes and low energy effective theory in Open String Theory
  3. Tree level gauge boson interactions in Open String Theory
  4. $3$ and $4$-point amplitudes
  5. Explicit structure of the low energy effective lagrangian up to ${\alpha'}^3$ order
  6. Low energy effective lagrangian up to ${\alpha'}^2$ terms
  7. Low energy effective lagrangian at ${\alpha'}^3$ order
  8. Basics of the conventional S-matrix approach to the low energy effective lagrangian
  9. Revisiting the S-matrix approach to the low energy effective lagrangian
  10. The basic idea of the method: An important constraint arises in the gauge boson amplitudes of Open Superstring Theory
  11. How the method works
  12. Applying the revisited S-matrix approach to obtain ${\cal L}_{\hbox{eff}}$ up to ${\alpha'}^3$ order
  13. Low energy effective lagrangian up to ${\alpha'}^2$ order
  14. Low energy effective lagrangian at ${\alpha'}^3$ order
  15. The low energy effective lagrangian at ${\alpha'}^4$ order
  16. ...and 18 more sections

Figures (3)

  • Figure 1: Feynman diagrams associated to the 5-point amplitude at ${\alpha'}^3$ order.
  • Figure 2: Feynman diagram that contributes to the 6-point amplitude at ${\alpha'}^4$ order. This diagram is responsible for fixing all the $a_j$ coefficients of ${\cal L}_{\hbox{eff}}^{(4)}$ without using any explicit information from Open Superstring Theory.
  • Figure 3: Feynman diagrams associated to the 6-point amplitude at ${\alpha'}^4$ order.