Generalized structures of ten-dimensional supersymmetric solutions

TL;DR

This paper extends the use of pure spinor techniques from 4D to general 10D supersymmetric solutions in type II string theories, deriving a unified system of differential equations for supersymmetry conditions.

Contribution

It introduces a generalized ISpin(7) structure framework for 10D solutions, unifying supersymmetry conditions in type II theories beyond specific spacetime geometries.

Findings

Derived a differential system equivalent to unbroken supersymmetry in 10D.

Unified pure spinor equations for 4D vacua within a 10D context.

Established a generalized geometric approach for supersymmetric solutions.

Abstract

Four-dimensional supersymmetric type II string theory vacua can be described elegantly in terms of pure spinors on the generalized tangent bundle T+T*. In this paper, we apply the same techniques to any ten-dimensional supersymmetric solution (not necessarily involving a factor with an AdS4 or Minkowski4 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.