D-branes on AdS flux compactifications

TL;DR

This paper develops a comprehensive framework for D-branes in ${\cal N}=1$ AdS$_4$ flux vacua, expressing D-brane supersymmetry as generalized calibration conditions defined on the full AdS$_4$ background. It shows how the AdS boundary and finite radius $R$ modify stability criteria, requiring a total calibration in nine dimensions and revealing a Breitenlohner-Freedman mechanism that stabilizes possible fluctuations. A precise 4D–10D dictionary is established by identifying D- and F-terms for space-filling branes, with F-flatness implying D-flatness in AdS$_4$, and explicit analyses are provided for SU(3)-structure, nearly Kähler IIA backgrounds. The work gives concrete, calibrated D-brane realizations in SU(3)-structure vacua and discusses implications for AdS/CFT including boundary effects and potential backreaction issues. Overall, it provides a robust geometric picture connecting bulk supersymmetry, calibrations, and D-brane energetics in AdS flux compactifications.

Abstract

We study D-branes in N=1 flux compactifications to AdS_4. We derive their supersymmetry conditions and express them in terms of background generalized calibrations. Basically because AdS has a boundary, the analysis of stability is more subtle and qualitatively different from the usual case of Minkowski compactifications. For instance, stable D-branes filling AdS_4 may wrap trivial internal cycles. Our analysis gives a geometric realization of the four-dimensional field theory approach of Freedman and collaborators. Furthermore, the one-to-one correspondence between the supersymmetry conditions of the background and the existence of generalized calibrations for D-branes is clarified and extended to any supersymmetric flux background that admits a time-like Killing vector and for which all fields are time-independent with respect to the associated time. As explicit examples, we discuss supersymmetric D-branes on IIA nearly Kaehler AdS_4 flux compactifications.

Figures (1)

• Figure 1: In both pictures the external AdS$_4$ is represented as a line segment, while the internal cycles are represented as circles. (a) Fluctuation that vanishes at the boundary. The shape of the deformed cycle $\Sigma'(\rho)$ depends on the location in AdS$_4$. Since the fluctuation is required to vanish at the boundary of AdS$_4$, the deformed cycle has to coincide there with the original cycle. (b) Homogeneous fluctuation. $\Sigma$ is homogeneously deformed into $\Sigma^\prime$, which means in particular that the deformation does not vanish at the boundary of AdS$_4$. Suppose ${\cal B}$ is the space between $\text{AdS}_4 \times \Sigma$ and $\text{AdS}_4 \times \Sigma^\prime$. From the picture it is clear that the boundary of ${\cal B}$ is not only the difference between the original D-brane and its deformation, but also includes a difference of boundary D-branes (shaded area).