The Geometry of Dyonic Instantons in 5-dimensional Supergravity

TL;DR

This paper constructs smooth supersymmetric solutions in 5D supergravity using ADHM instanton methods, revealing ring-like configurations with maximal angular momentum, and explores their physical properties and implications.

Contribution

It extends the ADHM construction to gravity-coupled systems, producing novel regular solutions interpreted as supertubes with bounded angular momentum.

Findings

Solutions are regular ring-like configurations in 5D supergravity.

Angular momentum is maximized for circular rings at fixed electric charge.

The solutions lack closed timelike curves, ensuring causality.

Abstract

We systematically construct and study smooth supersymmetric solutions in 5 dimensional N=1 Yang-Mills-Einstein supergravity. Our solution is based on the ADHM construction of (dyonic) multi-instantons in Yang-Mills theory, which extends to the gravity-coupled system. In a simple supergravity model obtained from N=2 theory, our solutions are regular ring-like configurations, which can also be interpreted as supertubes. By studying the SU(2) 2-instanton example in detail, we find that angular momentum is maximized, with fixed electric charge, for circular rings. This feature is qualitatively same as that of supertubes. Related to the existence of this upper bound of angular momentum, we also check the absence of closed timelike curves for the circular rings. Finally, in supergravity and gauge theory models with non-Abelian Chern-Simons terms, we point out that the solution in the symmetric phase carries electric charge which does not contribute to the energy. A possible explanation from the dynamics on the instanton moduli space is briefly discussed.