The Geometry of Dyonic Instantons in 5-dimensional Supergravity

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.