Generalized structures of ten-dimensional supersymmetric solutions

Four-dimensional supersymmetric type II string theory vacua can be described elegantly in terms of pure spinors on the generalized tangent bundle T circle plus T*. In this paper, we apply the same techniques to any ten-dimensional supersymmetric solution (not necessarily involving a factor with an AdS(4) or Minkowski(4) metric) in type II theories. We find a system of differential equations in terms of a form describing a "generalized ISpin(7) structure". This system is equivalent to unbroken supersymmetry, in both IIA and IIB. One of the equations reproduces in one fell swoop all the pure spinors equations for four-dimensional vacua.