On the Algebraic K-theory of The Massive D8 and M9 Branes

TL;DR

This paper explores the algebraic K-theory relationship between D8-branes in massive Type IIA supergravity and M9-branes in massive 11-dimensional supergravity, proposing a connection via K-theoretic maps.

Contribution

It introduces a novel K-theoretic framework linking D8-brane charges and M9-brane gauge fields across different supergravity theories.

Findings

Proposes a map between algebraic K-theory groups of D8- and M9-branes.

Suggests dimensional reduction as a tool to relate theories in different dimensions.

Connects brane charges to elements of K-theory groups.

Abstract

We study the relation between the D8-branes wrapped on an orientable compact manifold $W$ in a massive Type IIA supergravity background and the M9-branes wrapped on a compact manifold $Z$ in a massive d=11 supergravity background from the K-theoretic point of view. By speculating on the use of the dimensional reduction to relate the two theories in different dimensions and by interpreting the D8-brane charges as elements of $K_0 (C(W))$ and the (inequivalent classes of) spaces of gauge fields on the M9-branes as the elements of $K_0(C(Z)\times_{\bar{k}^*}G}$ a connection between charges and gauge fields is argued to exist. This connection is realized as a map between the corresponding algebraic K-theory groups.