Ninebrane structures

TL;DR

This paper introduces Ninebrane structures in degree twelve, extending the hierarchy of geometric structures related to anomaly cancellation in string and M-theory, and explores their variants and topological properties.

Contribution

It defines Ninebrane structures in degree twelve, links them to anomaly cancellation in M-theory, and discusses their variants, twists, and differential refinements.

Findings

Ninebrane structures capture anomaly cancellation phenomena in M-theory.

Variants called 2-Orientation and 2-Spin structures are introduced.

Topological groups associated with these structures are characterized.

Abstract

String structures in degree four are associated with cancellation of anomalies of string theory in ten dimensions. Fivebrane structures in degree eight have recently been shown to be associated with cancellation of anomalies associated to the NS5-brane in string theory as well as the M5-brane in M-theory. We introduce and describe "Ninebrane structures" in degree twelve and demonstrate how they capture some anomaly cancellation phenomena in M-theory. Along the way we also define certain variants, considered as intermediate cases in degree nine and ten, which we call "2-Orientation" and "2-Spin structures", respectively. As in the lower degree cases, we also discuss the natural twists of these structures and characterize the corresponding topological groups associated to each of the structures, which likewise admit refinements to differential cohomology.