Abstract
It is known that the anomalous Chern-Simons (CS) coupling of Op-plane is not consistent with the T-duality transformations. Compatibility of this coupling with the T-duality requires the inclusion of couplings involving one R-R field strength. In this paper we find such couplings at order α′2. By requiring the R-R and NS-NS gauge invariances, we first find all independent couplings at order α′2. There are 1, 6, 28, 20, 19, 2 couplings corresponding to the R-R field strengths F(p−4), F(p−2), F(p), F(p+2), F(p+4) and F(p+6), respectively. We then impose the T-duality constraint on these couplings and on the CS coupling C(p−3) ∧ R ∧ R at order α′2 to fix their corresponding coefficients. The T-duality constraint fixes all coefficients in terms of the CS coefficient. They are fully consistent with the partial couplings that have been already found in the literature by the S-matrix method.
Highlights
JHEP06(2020)171 type II superstring theories, including the Gibbons-Hawking-York boundary term [18, 19], can be rederived by the T-duality constraint
The T-duality constraint has been used in [30, 31] to find the effective action of Op-planes of type II superstring at order α 2 for NS-NS fields
We are interested in applying the T-duality constraint on the effective action of Op-plane when there is one R-R field strength
Summary
We would like to find minimum number of gauge invariant couplings on the world-volume of Op-plane involving one R-R field strength and an arbitrary number of NS-NS fields at order α 2, i.e., Sn. To find all gauge invariant and independent couplings involving one R-R field strength F (p), we first consider all contractions of one a0···ap, one F , ∇F or ∇∇F , odd number of H, ∇H and ∇∇H, and any number of ∇Φ, ∇∇Φ, ∇∇∇Φ, R, ∇R at four-derivative order. We impose the equations of motion, the O-plane conditions, the total derivative terms, and use the Bianchi identities and -tensor identities with the same strategy that is discussed in the subsection 2.1 In this manner one finds 20 independent couplings. Performing the same steps as in subsection 2.1, one finds there are 19 independent couplings on the world-volume of Op-plane that are not related to each other by the Bianchi identities, -tensor identities and the total derivative terms. We will find that all 76 parameters are fixed up to an overall factor
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