T-duality of D-brane versus O-plane actions

It is known that, in the static gauge, the world-volume and the transverse Kaluza-Klein (KK) reductions of the O-plane effective actions on a circle satisfy the T duality constraint for arbitrary base space background. In this paper we show that due to the presence of the second fundamental form in the D-brane couplings at order alpha' and higher, the T-duality is satisfied only for a subclass of the couplings for arbitrary base space background. They are m = 0 couplings where m is the number of B- tilde -field (without derivative on it). For m > 0 couplings, the base space metric must be block-diagonal and the momentum U(1) vector field in the transverse reduction must be zero. However, the derivatives of the metric and the vector field are arbitrary. Using the assumption that the effective actions at the critical dimension are background independent, we then show that the T-duality constraint for the couplings at order alpha' and for m = 0, fixes completely both bulk and boundary actions. These couplings indicate that the propagators of the massless open string fields receive alpha'-correction. We have also imposed the T-duality constraint on m = 1, 2, 3, 4 couplings. Because of the above restriction on the base space background in these cases, however, the T-duality can only partially fix the couplings for m > 0. This study shows that the Dirac-Born-Infeld (DBI) factor appears in both bulk and boundary actions at order alpha'.

Automated summary

This paper investigates the T-duality constraint on the world-volume and transverse Kaluza-Klein (KK) reductions of the O-plane effective actions on a circle in the static gauge. It is found that the T-duality is satisfied only for a subclass of the couplings with m = 0, where m is the number of B-tilde-field. For m > 0 couplings, certain conditions on the base space background must be satisfied. The study shows that the Dirac-Born-Infeld (DBI) factor appears in both bulk and boundary actions at order alpha'.