Abstract
For several classes of BPS vacua, we find a procedure to modify the PDEs that imply preserved supersymmetry and the equations of motion so that they still imply the latter but not the former. In each case we trace back this supersymmetry-breaking deformation to a distinct modification of the pure spinor equations that provide a geometrical interpretation of supersymmetry. We give some concrete examples: first we generalize the Imamura class of Mink6 solutions by removing a symmetry requirement, and then derive some local and global solutions both before and after breaking supersymmetry.
Highlights
Speaking, the hope would be to modify the aforementioned first-order geometrical systems, to obtain a new one that still implies the equations of motion (EoMs), when supplemented with the Bianchi identities, but which is no longer equivalent to the BPS conditions
For several classes of BPS vacua, we find a procedure to modify the PDEs that imply preserved supersymmetry and the equations of motion so that they still imply the latter but not the former
In each case we trace back this supersymmetry-breaking deformation to a distinct modification of the pure spinor equations that provide a geometrical interpretation of supersymmetry
Summary
In subsequent subsections we will get more specific and present some interesting subclasses of solutions, whose supersymmetry we will break later in the paper. As we anticipated in the introduction, we are interested in Minkd × M10−d solutions with d ≥ 4 in type II supergravity. Solutions with higher-dimensional external space are included by further splitting M6: ds2(M6) = e2Ads2(Rd) + ds2(M6−d). In order to preserve the Poincaré isometries of Mink, we have to assume that the warping function A only depends on the six-dimensional manifold M6 (or on M6−d, if we are considering the case (2.2)). In this paper we will not use directly the spinorial formalism, but we will appeal to the pure spinor method, which allows to reformulate the problem of finding four-dimensional vacuum solutions
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