Geometry of a desingularization of eleven-dimensional gravitational spinors

TL;DR

This paper constructs a geometric desingularization of the space of eleven-dimensional gravitational spinors, revealing a fiber bundle structure over an isotropic Grassmannian and reformulating supergravity equations as Cauchy-Riemann equations.

Contribution

It introduces a geometric desingularization of the gravitational spinor space in eleven dimensions and connects supergravity equations to complex geometric structures.

Findings

Desingularization fibers over OGr(2,11)

Reformulation of supergravity equations as Cauchy-Riemann equations

Provides geometric insights into eleven-dimensional spinors

Abstract

We show that the space of gravitational spinors in eleven dimensions, defined by equations $\Gamma_{\alpha\beta}^i\lambda^{\alpha}\lambda^{\beta}=0$ admits a desingularization with nice geometric properties. In particular the desingularization fibers over the isotropic Grassmannian OGr(2,11). This enables us to recast equations of linearized eleven-dimensional supergravity adapted to 3-form potential into Cauchy-Riemann equations on a super extension of isotropic Grassmannian OGr(2,11).