Branes on Generalized Calibrated Submanifolds

Abstract

We extend previous results on generalized calibrations to describe supersymmetric branes in supergravity backgrounds with diverse fields turned on, and provide several new classes of examples. As an important application, we show that supersymmetric D-branes in compactifications with field strength fluxes, and on SU(3)-structure spaces, wrap generalized calibrated submanifolds, defined by simple conditions in terms of the underlying globally defined, but non-closed, 2- and 3-forms. We provide examples where the geometric moduli of D-branes (for instance D7-branes in 3-form flux configurations) are lifted by the generalized calibration condition. In addition, we describe supersymmetric D6-branes on generalized calibrated 3-submanifolds of half-flat manifolds, which provide the mirror of B-type D-branes in IIB CY compactifications with 3-form fluxes. Supersymmetric sets of such D-branes carrying no homology charges are mirror to supersymmetric sets of D-branes which are homologically non-trivial, but trivial in K-theory. As an additional application, we describe models with chiral gauge sectors, realized in terms of generalized calibrated brane box configurations of NS- and D5-branes, which are supersymmetric but carry no charges, so that no orientifold planes are required in the compactification.

Figures (3)

• Figure 1: The D5-branes wrap an $S^2$ in $S^5$, which is cut in four quadrants by its intersection with the NS- and NS'-brane $S^2$'s.
• Figure 2: North and South pole views of the $S^2$ spanned by the D5-branes. The numbers label the gauge groups arising from D5-branes in each quadrant, while the arrows denote chiral multiplets arising from the brane box intersections. Notice that the gluing of the two half-spheres makes some of the arrows in the picture redundant.
• Figure 3: North and South pole view of the calibrated branes in the brane diamond configuration.