E8 Gauge Theory, and a Derivation of K-Theory from M-Theory

TL;DR

This paper compares phase factors in Type IIA supergravity and M-theory, confirming duality and linking K-theory to E8 gauge theory, while revealing insights into D-brane stability and anomaly conditions.

Contribution

It demonstrates the equivalence of phase factors in M-theory and Type IIA supergravity, establishing a connection between K-theory and E8 gauge theory within the duality framework.

Findings

Phase factors in M-theory and Type IIA match, supporting duality.

Certain wrapped D-brane states are unstable.

Type IIA theory is consistent only if W_7=0.

Abstract

The partition function of Ramond-Ramond p-form fields in Type IIA supergravity on a ten-manifold X contains subtle phase factors that are associated with T-duality, self-duality, and the relation of the RR fields to K-theory. The analogous partition function of M-theory on X x S1 contains subtle phases that are similarly associated with E8 gauge theory. We analyze the detailed phase factors on the two sides and show that they agree, thereby testing M-theory/Type IIA duality as well as the K-theory formalism in an interesting way. We also show that certain D-brane states wrapped on nontrivial homology cycles are actually unstable, that (-1)^{F_L} symmetry in Type IIA superstring theory depends in general on a cancellation between a fermion anomaly and an anomaly of RR fields, and that Type IIA superstring theory with no wrapped branes is well-defined only on a spacetime with W_7=0.