Type IIA Killing spinors and calibrations

Abstract

We consider the dimensional reduction of eleven dimensional supergravity to type IIA in ten dimensions, and study the conditions for supersymmetry in terms of p-form spinor bi-linears of the supersymmetry parameter. For a bosonic solution to be supersymmetric these p-forms must satisfy a set of differential relations, which we derive in full; the supersymmetry variations of the dilatino give a set of algebraic relations which are also derived. These results are then used to provide the generalized calibration conditions for some of the basic brane solutions, we also follow up a suggestion of Hackett-Jones and Smith and present a calibration condition for IIA supertubes. We find that a probe supertube satisfies this bound but does not saturate it, with the bound successfully accounting for the D0 charge of the supertube but not the string charge; we speculate that there should be a stronger calibration inequality than the one given.