5D fuzzball geometries and 4D polar states

TL;DR

This paper explores the connection between five-dimensional fuzzball solutions and four-dimensional multicentered configurations, revealing how certain microstates of black rings correspond to polar states with D6 branes, and analyzing the effects of spectral flow transformations.

Contribution

It provides a detailed mapping between 5D fuzzball geometries and 4D polar states, extending the understanding of microstate structure and flux configurations in black hole physics.

Findings

5D Kaluza-Klein monopole supertubes correspond to 4D D6/anti-D6 polar states.

4D configurations are zero-entropy constituents of multi-centered systems.

Spectral flow in 5D induces flux variations in 4D polar configurations.

Abstract

We analyze the map between a class of `fuzzball' solutions in five dimensions and four-dimensional multicentered solutions under the 4D-5D connection, and interpret the resulting configurations in the framework of Denef and Moore. In five dimensions, we consider Kaluza-Klein monopole supertubes with circular profile which represent microstates of a small black ring. The resulting four-dimensional configurations are, in a suitable duality frame, polar states consisting of stacks of D6 and anti-D6 branes with flux. We argue that these four-dimensional configurations represent zero-entropy constituents of a 2-centered configuration where one of the centers is a small black hole. We also discuss how spectral flow transformations in five dimensions, leading to configurations with momentum, give rise to four-dimensional D6 anti-D6 polar configurations with different flux distributions at the centers.