Existence of hyperbolic calorons

@article{Sibner2015ExistenceOH,
  title={Existence of hyperbolic calorons},
  author={Lesley M. Sibner and Robert J. Sibner and Yisong Yang},
  journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  year={2015},
  volume={471}
}
  • L. SibnerR. SibnerYisong Yang
  • Published 4 March 2015
  • Mathematics
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Recent work of Harland shows that the SO(3)-symmetric, dimensionally reduced, charge-N self-dual Yang–Mills calorons on the hyperbolic space H3×S1 may be obtained through constructing N-vortex solutions of an Abelian Higgs model as in the study of Witten on multiple instantons. In this paper, we establish the existence of such minimal action charge-N calorons by constructing arbitrarily prescribed N-vortex solutions of the Witten type equations. 

References

SHOWING 1-10 OF 27 REFERENCES

Hyperbolic Calorons, Monopoles, and Instantons

We construct families of SO(3)-symmetric charge 1 instantons and calorons on the space $${\mathbb{H}^3 \times \mathbb{R}}$$ . We show how the calorons include instantons and hyperbolic monopoles as

Classical solutions of SU (2) Yang--Mills theories

A comprehensive review of the known classical solutions of $\mathrm{SU}(2)$ gauge theories is presented. The author follows the historical development of this subject from its beginning (the first

N‐dimensional instantons and monopoles

The possibility of finding solutions of the instanton and monopole types to gauge field theories on arbitrary even and odd dimensional Euclidean manifolds respectively is investigated. Suitable

Multiple Instantons Representing Higher-Order Chern–Pontryagin Classes, II

This paper is a continuation of an earlier study on the generalized Yang–Mills instantons over 4m-dimensional spheres. We will first present a discussion on the generalized Yang–Mills equations, the

Singular instantons with SO(3) symmetry

This article provides an explicit construction for a family of singular instantons on S^4 S^2 with arbitrary real holonomy parameter \alpha. This family includes the original \alpha = 1/4, c_2 = 3/2

Multiple Instantons Representing Higher-Order Chern–Pontryagin Classes

Abstract:It has been shown in the work of Chakrabarti, Sherry and Tchrakian that the chiral SO±(4 p) Yang–Mills theory in the Euclidean 4 p (p≥ 2) dimensions allows an axially symmetric self-dual

Zero and Infinite Curvature Limits of Hyperbolic Monopoles

We show that the zero curvature limit of the space of hyperbolic monopoles gives the Euclidean monopoles, settling a conjecture of Atiyah. We also study the infinite curvature limit of the space of

Geometry of hyperbolic monopoles

The hyperbolic monopoles of Atiyah [M. F. Atiyah, Commun. Math. Phys. 93, 471 (1984); ‘‘Magnetic monopoles in hyperbolic space,’’ in Proceedings of the International Colloquium on Vector Bundles

Some exact multipseudoparticle solutions of classical Yang--Mills theory

I present some exact solutions of the Polyakov--Belavin--Schwartz--Tyupkin equation F/sub ..mu nu../ =F/sub ..mu..//sub ..nu../ for an SU(2) gauge theory in Euclidean space. My solutions describe a

THE SELF-DUALITY EQUATIONS ON A RIEMANN SURFACE

In this paper we shall study a special class of solutions of the self-dual Yang-Mills equations. The original self-duality equations which arose in mathematical physics were defined on Euclidean