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

Abstract

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 α′ 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 $$ \overset{\sim }{B} $$ B ~ -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 α′ and for m = 0, fixes completely both bulk and boundary actions. These couplings indicate that the propagators of the massless open string fields receive α′-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 α′.

Effective action of type II superstring theories at order α′3: NS-NS couplings

“…It is under this specific background of the base space that the effective action of the D-brane satisfies the aforementioned constraint. Consequently, the T-duality constraint on only the massless closed string fields cannot fully fix the world-volume couplings [31] 2 . On the other hand, the T-duality constraint on only the massless open string fields cannot fully fix the world-volume couplings, up to overall factors, either [32,33].…”

“…Note that in[31], we were not aware at that time that setting the world-volume components of the momentum vector field to zero in the transverse reduction is equivalent to imposing the U (1) × U (1) gauge symmetry on the covariant coupling in the transverse reduction.3 Note that the world-sheet action of a string in the presence of a background B-field incorporates the 2-dimensional antisymmetric Levi-Civita tensor. As a result, the B-field exhibits an odd behavior under worldsheet parity.…”