From wrapped M-branes to Calabi-Yau black holes and strings

TL;DR

This paper explores M-branes wrapping cycles in Calabi-Yau manifolds, analyzing their supersymmetry constraints and connecting 11-dimensional solutions to known 5-dimensional black hole and string solutions, with implications for non-linear reductions.

Contribution

It provides a detailed analysis of supersymmetric M-brane configurations and extends the understanding of their dimensional reduction beyond the linear approximation.

Findings

Dimensional reduction yields known 5D black hole and string solutions.

Supersymmetry constraints relate 11D M-branes to 5D supergravity.

Extension beyond linear regime aids in constructing non-linear Calabi-Yau reductions.

Abstract

We study a class of D=11 BPS spacetimes that describe M-branes wrapping supersymmetric 2 and 4-cycles of Calabi-Yau 3-folds. We analyze the geometrical significance of the supersymmetry constraints and gauge field equations of motion for these spacetimes. We show that the dimensional reduction to D=5 yields known BPS black hole and black string solutions of D=5, N=2 supergravity. The usual ansatz for the dimensional reduction is valid only in the linearized regime of slowly varying moduli and small gauge field strengths. Our identification of the massless D=5 modes with D=11 quantities extends beyond this regime and should prove useful in constructing non-linear ansatze for Calabi-Yau dimensional reductions of supergravity theories.