Compactifying M-Theory to Four Dimensions

TL;DR

This paper explores how M-theory can be compactified to four dimensions using non-compact seven-dimensional manifolds with warp factors influenced by fivebranes, providing explicit solutions and field strength expressions.

Contribution

It introduces a new class of M-theory compactifications on non-compact manifolds with non-constant warp factors due to fivebrane sources, including explicit solutions.

Findings

Derived explicit expressions for field strengths.

Constructed specific examples of the compactifications.

Analyzed the impact of fivebrane sources on warp factors.

Abstract

We consider compactifications of ${\cal M}$-theory to four-dimensional Minkowski space on seven-dimensional non-compact manifolds. These compactifications include a warp factor which is non-constant due to the presence of sources coming from fivebranes wrapping two-dimensional submanifolds of the internal seven-dimensional space. We derive the expression for the field strengths and consider an explicit example of this general class of solutions.