Split Flows in Bubbled Geometries

TL;DR

This paper introduces a new procedure using tree-like skeleton graphs to analyze the physical sectors of five-dimensional bubbled geometries, ensuring the absence of closed timelike curves and clarifying solution existence.

Contribution

It proposes a novel skeleton-based method to identify physical solutions in bubbled geometries, extending ideas from split attractor flows without relying on moduli space.

Findings

Skeleton existence correlates with local CTC conditions.

Numerical examples demonstrate the procedure's effectiveness.

Charge parameters are constrained by existence conditions.

Abstract

We propose a procedure to clarify part of the physical sector in the five dimensional bubble geometries based on ideas similar to the split attractor flow conjecture proposed by Denef. This procedure involves building some simple tree-like graphs that we call skeletons without referring to the moduli space. The skeleton (tree) exists if and only if it passes the existence conditions which are purely based on some local CTC's (closed timelike curves) checking. Then, we propose the conjecture similar to Denef's version which states that every existing skeleton (tree) should correspond to some solution in which the global absence of CTC's is ensured. Furthermore, we propose two pictures to identify this correspondence explicitly and use some numerical examples to show how this procedure works. We also analyze the physical sector of the simplest bubbled supertube and see how the existence conditions constrain the charge parameter space.