Calibrations and Intersecting Branes

TL;DR

This paper explores supersymmetric solutions of calibration-related actions and their interpretation as intersecting branes, revealing how preserved supersymmetry relates to subgroup spinor singlets and introducing new solutions with 1/8 supersymmetry.

Contribution

It provides a detailed analysis of supersymmetry preservation in calibration solutions and introduces new worldvolume solutions with partial supersymmetry.

Findings

Supersymmetry preservation linked to subgroup spinor singlets.

Worldvolume solutions can preserve 1/8 of bulk supersymmetry.

Bulk interpretation of solutions as intersecting branes.

Abstract

We investigate the solutions of Nambu-Goto-type actions associated with calibrations. We determine the supersymmetry preserved by these solutions using the contact set of the calibration and examine their bulk interpretation as intersecting branes. We show that the supersymmetry preserved by such solutions is closely related to the spinor singlets of the subgroup $G$ of $Spin (9,1)$ or $Spin (10,1)$ that rotates the tangent spaces of the brane. We find that the supersymmetry projections of the worldvolume solutions are precisely those of the associated bulk configurations. We also investigate the supersymmetric solutions of a Born-Infeld action. We show that in some cases this problem also reduces to counting spinor singlets of a subgroup of $Spin (9,1)$ acting on the associated spinor representations. We also find new worldvolume solutions which preserve 1/8 of the supersymmetry of the bulk and give their bulk interpretation.