An approach to anomalies in M-theory via KSpin

TL;DR

This paper explores anomalies in M-theory through the lens of Spin K-theory, revealing cohomological structures, reinterpretations of the one-loop term, and natural anomaly interpretations, emphasizing the role of mod 3 reductions.

Contribution

It introduces a Spin K-theoretic framework to understand M-theory anomalies, connecting cohomology, characteristic classes, and homotopy invariance.

Findings

Cohomological properties of M-theory fields fit into Spin K-theory.

The one-loop term is homotopy invariant when expressed via Spin characteristic classes.

Anomalies in M-theory have natural interpretations within Spin K-theory, with mod 3 reductions playing a key role.

Abstract

The M-theory fieldstrength and its dual, given by the integral lift of the left hand side of the equation of motion, both satisfy certain cohomological properties. We study the combined fields and observe that the multiplicative structure on the product of the corresponding degree four and degree eight cohomology fits into that given by Spin K-theory. This explains some earlier results and leads naturally to the use of Spin characteristic classes. We reinterpret the one-loop term in terms of such classes and we show that it is homotopy invariant. We argue that the various anomalies have natural interpretations within Spin K-theory. In the process, mod 3 reductions play a special role.