The lift of type IIA supergravity with D6 sources: M-theory with torsion

TL;DR

This paper extends the Kaluza-Klein framework to include D6-brane sources in type IIA supergravity, deriving modified equations of motion in M-theory with torsion and their reduction to type IIA.

Contribution

It introduces a method to incorporate D6-brane sources into the Kaluza-Klein reduction, addressing the breakdown of the standard formalism and deriving source-modified equations.

Findings

Derived source-modified equations of motion in M-theory with torsion.

Obtained type IIA equations with D6 sources via dimensional reduction.

Addressed the breakdown of the standard KK formalism in the presence of sources.

Abstract

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.