Topological Transitions and Enhancon-like Geometries in Calabi-Yau Compactifications of M-Theory

TL;DR

This paper investigates how topological phase transitions in Calabi-Yau threefolds affect five-dimensional black hole and black string geometries in M-theory, revealing conditions for regular solutions and connections to enhancon-like phenomena.

Contribution

It demonstrates that solutions can be continued through topological transitions and identifies conditions under which singularities are resolved in M-theory compactifications.

Findings

Solutions can be continued across flop transitions and gauge symmetry enhancements.

Black string solutions remain non-singular within the Kahler cone.

Black hole solutions over certain elliptic fibrations are regularized via enhancon mechanisms.

Abstract

We study the impact of topological phase transitions of the internal Calabi-Yau threefold on the space-time geometry of five-dimensional extremal black holes and black strings. For flop transitions and SU(2) gauge symmetry enhancement we show that solutions can always be continued and that the behaviour of metric, gauge fields and scalars can be characterized in a model independent way. Then we look at supersymmetric solutions which describe naked singularities rather than geometries with a horizon. For black strings we show that the solution cannot become singular as long as the scalar fields take values inside the Kahler cone. For black holes we establish the same result for the elliptic fibrations over the Hirzebruch surfaces F_0, F_1, F_2. These three models exhibit a behaviour similar to the enhancon, since one runs into SU(2) enhancement before reaching the apparent singularity. Using the proper continuation inside the enhancon radius one finds that the solution is regular.