On NS-NS couplings at order [formula omitted

Abstract

Recently, imposing the gauge-symmetry and the T-duality constraints on the string frame effective actions of type II superstring theories at order α′3, the NS-NS couplings 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, Hαβμ and ∇αHβμν. The number of couplings in the structures R4, H8, H6R, H4R2, H2R3 are 2, 2, 1, 7, 22, respectively, and the number of couplings in the structures (∇H)4, (∇H)2R2, (∇H)2H4, (∇H)2H2R are 12, 22, 77, 106, respectively. The new couplings are also fully consistent with the sphere-level S-matrix element of four NS-NS vertex operators.