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5-field terms in the open superstring effective action

Luiz Antonio Barreiro, Ricardo Medina

TL;DR

This work derives, for open superstrings, the full set of non-abelian five-field interaction terms in the low-energy effective action to all orders in $\alpha'$, by exploiting the tree-level five-point amplitude. Starting from the known YM and $F^4$-type structures, the authors decompose the 5-point amplitude into two building blocks, $T$ and $K_3$, and isolate no-pole, gauge-invariant contributions that map to a local Lagrangian for the $D^{2n}F^5$ sector. They provide a closed-form expression for ${\cal L}_{D^{2n}F^5}$ in terms of $t_{(8)}$ and a new $t_{(10)}$ tensor, with explicit $\alpha'$-expansions up to high orders and concrete checks against existing $O(\alpha'^3)$ results. The findings advance the program of obtaining all-$\alpha'$ corrections from string scattering data and have implications for D-brane dynamics and Type I theories, while laying groundwork for potential connections to closed-string sectors via KLT relations.

Abstract

Some time ago the bosonic and fermionic 4-field terms of the non-abelian low energy effective action of the open superstring were obtained, to all order in $α'$. This was done at tree level by directly generalizing the abelian case, treated some time before, and considering the known expressions of all massless superstring 4-point amplitudes (at tree level). In the present work we obtain the bosonic 5-field terms of this effective action, to all order in $α'$. This is done by considering the simplified expression of the superstring 5-point amplitude for massless bosons, obtained some time ago.

5-field terms in the open superstring effective action

TL;DR

This work derives, for open superstrings, the full set of non-abelian five-field interaction terms in the low-energy effective action to all orders in , by exploiting the tree-level five-point amplitude. Starting from the known YM and -type structures, the authors decompose the 5-point amplitude into two building blocks, and , and isolate no-pole, gauge-invariant contributions that map to a local Lagrangian for the sector. They provide a closed-form expression for in terms of and a new tensor, with explicit -expansions up to high orders and concrete checks against existing results. The findings advance the program of obtaining all- corrections from string scattering data and have implications for D-brane dynamics and Type I theories, while laying groundwork for potential connections to closed-string sectors via KLT relations.

Abstract

Some time ago the bosonic and fermionic 4-field terms of the non-abelian low energy effective action of the open superstring were obtained, to all order in . This was done at tree level by directly generalizing the abelian case, treated some time before, and considering the known expressions of all massless superstring 4-point amplitudes (at tree level). In the present work we obtain the bosonic 5-field terms of this effective action, to all order in . This is done by considering the simplified expression of the superstring 5-point amplitude for massless bosons, obtained some time ago.

Paper Structure

This paper contains 27 sections, 78 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Review of scattering amplitudes and low energy effective lagrangian
  3. 3 and 4-point subamplitudes and their effective lagrangian in Open Superstring Theory
  4. The 5-point amplitude of massless bosons in Open Superstring Theory
  5. Review of the 5-point subamplitude derivation
  6. Properties satisfied by the 5-point amplitude
  7. 5-field terms in the low energy effective lagrangian
  8. The $D^{2n}F^5$ terms 5-point subamplitude
  9. The main formula
  10. Some $\alpha'$ terms
  11. Summary and final remarks
  12. Conventions and identities
  13. Tensors
  14. $t_{(8)}$ and $(\eta \cdot t_{(8)})_1$ tensors
  15. $t_{(10)}$ tensor
  16. ...and 12 more sections

Figures (1)

  • Figure 2: Type of 5-particle diagrams, with $\alpha'$ dependence, which come from the effective lagrangian. The Feynman diagram in (a) is one particle irreducible (1 PI), while the one in (b) is one particle reducible.