Magnetically Charged Calorons with Non-Trivial Holonomy

Instantons in pure Yang-Mills theories on partially periodic space $\mathbb{R}^3\times S^1$ are usually called calorons. The background periodicity brings on characteristic features of calorons such as non-trivial holonomy, which plays an essential role for confinement/deconfinement transition in pure Yang-Mills gauge theory. For the case of gauge group $SU(2)$, calorons can be interpreted as composite objects of two constituent "monopoles" with opposite magnetic charges. There are often the cases that the two monopole charges are unbalanced so that the calorons possess net magnetic charge in $\mathbb{R}^3$. In this paper, we consider several mechanism how such net magnetic charges appear for certain types of calorons through the ADHM/Nahm construction with explicit examples. In particular, we construct analytically the gauge configuration of the $(2,1)$-caloron with $U(1)$-symmetry, which has intrinsically magnetic charge.Comment: 33 pages, 8 figure

Skyrmions, Skyrme stars and black holes with Skyrme hair in five spacetime dimension

We consider a class of generalizations of the Skyrme model to five spacetime dimensions (d = 5), which is de fined in terms of an O (5) sigma model. A special ansatz for the Skyrme field allows angular momentum to be present and equations of motion with a radial dependence only. Using it, we obtain: 1) everywhere regular solutions describing localised energy lumps (Skyrmions); 2) Self-gravitating, asymptotically flat, everywhere non-singular solitonic solutions (Skyrme stars), upon minimally coupling the model to Einstein's gravity; 3) both static and spinning black holes with Skyrme hair, the latter with rotation in two orthogonal planes, with both angular momenta of equal magnitude. In the absence of gravity we present an analytic solution that satisfies a BPS-type bound and explore numerically some of the non-BPS solutions. In the presence of gravity, we contrast the solutions to this model with solutions to a complex scalar field model, namely boson stars and black holes with synchronised hair. Remarkably, even though the two models present key differences, and in particular the Skyrme model allows static hairy black holes, when introducing rotation, the synchronisation condition becomes mandatory, providing further evidence for its generality in obtaining rotating hairy black holes