This paper is concerned with an extension of the well known Kaluza-Klein
mechanism. As the standard ansatz for Kaluza-Klein reduction implies the
existence of a gauge potential associated with the KK field strength, it
follows immediately that this field strength satisfies its Bianchi identity.
Hence, the standard KK formalism breaks down in the presence of a violated
Bianchi identity. This occurs for example in the context of D6 sources.
We will investigate and partially solve this problem in the context of the
type IIA/M-theory duality. Our discussion is motivated by the construction of
gauge/string duals with backreacting flavor branes using D6-branes, which
appear in M-theory as KK-monopoles. We are able to derive source-modified
equations of motion for the eleven-dimensional theory, and are subsequently
able to obtain the source-modified type IIA equations by direct dimensional
reduction.Comment: 25 pages plus appendices - As published in JHE