On NS-NS couplings at order $\alpha'^3$

TL;DR

This paper refines the NS-NS couplings in type II superstring effective actions at order α'^3, reducing the number of couplings and expressing them in terms of Riemann curvature and H-field derivatives, consistent with string S-matrix results.

Contribution

It presents a reorganization of NS-NS couplings using field redefinitions, decreasing the couplings from 445 to 251 and expressing them in terms of fewer structures involving R and H fields.

Findings

Reduced couplings from 445 to 251 using field redefinitions.

Expressed couplings in terms of 9 structures involving R and H derivatives.

Confirmed consistency with sphere-level S-matrix calculations.

Abstract

Recently, imposing the gauge-symmetry and the T-duality constraints on the string frame effective actions of type II superstring theories, the NS-NS cuplings have been found in a particular scheme which has 445 couplings in 15 different structures. In this paper, using a field redefinition, we write them in terms of 251 couplings which appear in 9 different structures. The 9 structures involve only Riemann curvature, $H_{\alpha\beta\mu}$ and $\nabla_{\alpha}H_{\beta\mu\nu}$. The number of couplings in the structures $R^4$, $H^8$, $H^6R$, $H^4R^2$, $H^2R^3$ are $2,\, 2,\, 1,\, 7,\,22$, respectively, and the number of couplings in the structures $(\nabla H)^4$, $(\nabla H)^2 R^2$, $(\nabla H)^2 H^4$, $(\nabla H)^2H^2R$ are $12,\, 22,\, 77,\, 106$, respectively. The new couplings are fully consistent with the sphere-level S-matrix element of four NS-NS vertex operators.