Bubbles on Manifolds with a U(1) Isometry

TL;DR

This paper constructs five-dimensional supergravity solutions with a U(1) isometry using warped compactifications on singular hyper-Kahler bases, demonstrating regularity and new bubbling solutions.

Contribution

It introduces a method to obtain regular five-dimensional supergravity solutions from singular hyper-Kahler base spaces with a U(1) isometry, including explicit solutions and bubbling procedures.

Findings

Explicit supersymmetric solutions from Atiyah-Hitchin base

Regularity around the ambi-polar base's critical surface

Bubbling procedure transforming Eguchi-Hanson space into AdS_2xS^3

Abstract

We investigate the construction of five-dimensional, three-charge supergravity solutions that only have a rotational U(1) isometry. We show that such solutions can be obtained as warped compactifications with a singular ambi-polar hyper-Kahler base space and singular warp factors. We show that the complete solution is regular around the critical surface of the ambi-polar base. We illustrate this by presenting the explicit form of the most general supersymmetric solutions that can be obtained from an Atiyah-Hitchin base space and its ambi-polar generalizations. We make a parallel analysis using an ambi-polar generalization of the Eguchi-Hanson base space metric. We also show how the bubbling procedure applied to the ambi-polar Eguchi-Hanson metric can convert it to a global AdS_2xS^3 compactification.