4-point effective actions in open and closed superstring theory

TL;DR

This paper extends the explicit construction of 4-point effective actions from abelian open superstring theory to nonabelian cases and derives the all-order effective action for closed superstring theory's NS-NS sector.

Contribution

It generalizes the 4-point effective action to nonabelian open superstring theory and derives the all-order effective action for closed superstring NS-NS sector.

Findings

Agreement with existing results at ${eta'}^3$ and ${eta'}^4$ orders

Explicit nonabelian 4-point effective action constructed

All-order effective action for closed superstring NS-NS sector derived

Abstract

Recently the effective action for the 4-point functions in abelian open superstring theory has been derived, giving an explicit construction of the bosonic and fermionic terms of this infinite $\alpha'$ series. In the present work we generalize this result to the nonabelian case. We test our result, at ${\alpha'}^3$ and ${\alpha'}^4$ order, with several existing versions for these terms, finding agreement in most of the cases. We also apply these ideas to derive the effective action for the 4-point functions of the NS-NS sector of closed superstring theory, to all order in $\alpha'$.