4-point effective actions in open and closed superstring theory

Recently the effective action for the 4-point functions in abelian open super-string theory has been derived, giving an explicit construction of the bosonic and fermionic terms of this infinite α′ series. In the present work we generalize this result to the non-abelian case. We test our result, at α′³ and α′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 α′.