Branes and fluxes in D=5 Calabi–Yau compactifications of M-theory

We discuss Poincaré three-brane solutions in D=5 M-theory compactifications on Calabi–Yau (CY) threefolds with G-fluxes. We show that the vector moduli freeze at an attractor point. In the case with background flux only, the spacetime geometry contains a zero volume singularity with the three-brane and the CY space shrinking simultaneously to a point. This problem can be avoided by including explicit three-brane sources. We consider two cases in detail: a single brane and, when the transverse dimension is compactified on a circle, a pair of branes with opposite tensions.