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

TL;DR

This paper investigates how T-duality constrains D-brane and O-plane effective actions, revealing that certain couplings are fixed by T-duality at order α' and highlighting the role of the Dirac-Born-Infeld factor.

Contribution

It demonstrates that T-duality constrains D-brane couplings at order α', fixing bulk and boundary actions for m=0 couplings, and clarifies conditions for partial fixing of couplings with m>0.

Findings

T-duality fully constrains m=0 couplings at order α'

For m>0, T-duality imposes restrictions on the background metric and fields

The Dirac-Born-Infeld factor appears at order α' in both bulk and boundary 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 $\alpha'$ and higher, the T-duality is satisfied only for a subclass of couplings for arbitrary base space background. They are $m=0$ couplings where $m$ is the number of $\tilde{B}$-field (without derivative on it). For $m>0$ couplings, the base space metric must be block-diagonal and the momentum $U(1)$ vector field 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 $\alpha'$.