Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The geometry of extended null supersymmetry in M-theory   For supersymmetric spacetimes in eleven dimensions admitting a null Killing
spinor, a set of explicit necessary and sufficient conditions for the existence
of any number of arbitrary additional Killing spinors is derived. The necessary
and sufficient conditions are comprised of algebraic relationships, linear in
the spinorial components, between the spinorial components and their first
derivatives, and the components of the spin connection and four-form. The
integrability conditions for the Killing spinor equation are also analysed in
detail, to determine which components of the field equations are implied by
arbitrary additional supersymmetries and the four-form Bianchi identity. This
provides a complete formalism for the systematic and exhaustive investigation
of all spacetimes with extended null supersymmetry in eleven dimensions. The
formalism is employed to show that the general bosonic solution of eleven
dimensional supergravity admitting a $G_2$ structure defined by four Killing
spinors is either locally the direct product of $\mathbb{R}^{1,3}$ with a
seven-manifold of $G_2$ holonomy, or locally the Freund-Rubin direct product of
$AdS_4$ with a seven-manifold of weak $G_2$ holonomy. In addition, all
supersymmetric spacetimes admitting a
$(G_2\ltimes\mathbb{R}^7)\times\mathbb{R}^2$ structure are classified.

28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph