arXiv subjects

Derek Harland

Publications and source records attributed to Derek Harland.

43 records · Page 3Linked to original sources

arXiv2010

Kinks, chains, and loop groups in the CP^n sigma models

We consider topological solitons in the CP^n sigma models in two space dimensions. In particular, we study "kinks", which are independent of one coordinate up to a rotation of the target space, and "chains", which are periodic in one coordinate up to a rotation of the target space. Kinks and chains both exhibit constituents, similar to monopoles and calorons in SU(n) Yang-Mills-Higgs and Yang-Mills theories. We examine the constituent structure using Lie algebras.

hep-th↗

arXiv2009

Equivariant reduction of Yang-Mills theory over the fuzzy sphere and the emergent vortices

We consider a U(2) Yang-Mills theory on M x S_F^2 where M is a Riemannian manifold and S_F^2 is the fuzzy sphere. Using essentially the representation theory of SU(2) we determine the most general SU(2)-equivariant gauge field on M x S_F^2. This allows us to reduce the Yang-Mills theory on M x S_F^2 down to an abelian Higgs-type model over M. Depending on the enforcement (or non-enforcement) of a "constraint" term, the latter may (or may not) lead to the standard critically-coupled abelian Higgs model in the commutative limit, S_F^2 -> S^2. For M = R^2, we find that the abelian Higgs-type model admits vortex solutions corresponding to instantons in the original Yang-Mills theory. Vortices are in general no longer BPS, but may attract or repel according to the values of parameters.

hep-th↗

arXiv2009

Dynamics of Periodic Monopoles

BPS monopoles which are periodic in one of the spatial directions correspond, via a generalized Nahm transform, to solutions of the Hitchin equations on a cylinder. A one-parameter family of solutions of these equations, representing a geodesic in the 2-monopole moduli space, is constructed numerically. It corresponds to a slow-motion dynamical evolution, in which two parallel monopole chains collide and scatter at right angles.

hep-th↗

arXiv2008

Hyperbolic calorons, monopoles, and instantons

We construct families of SO(3)-symmetric charge 1 instantons and calorons on the space H^3 x R. We show how the calorons include instantons and hyperbolic monopoles as limiting cases. We show how Euclidean calorons are the flat space limit of this family.

hep-th↗

arXiv2008

Chains of Skyrmions

Skyrme chains are topologically-nontrivial solutions of the Skyrme model which are (quasi-)periodic in one spatial direction. We report numerical and analytic investigations which show that such solutions exist. Chains of 1-skyrmions are reasonably well approximated both as parallel vortex-antivortex pairs, and in terms of the holonomy of Yang-Mills calorons. As the period increases, the 1-skyrmions clump together, for example giving chains of 2-skyrmions or 4-skyrmions.

hep-th↗

arXiv2007

Walls and chains of planar skyrmions

In planar (baby) Skyrme systems, there may be extended linear structures which resemble either domain walls or chains of skyrmions, depending on the choice of potential and boundary conditions. We show that systems with a single vacuum, for example with potential V=1-phi_3, admit chain solutions, whereas walls are ruled out by the uniqueness of the vacuum. On the other hand, in double-vacuum systems such as V=1/2*(1-phi_3^2), one has stable wall solutions, but there are no stable chains; the walls may be viewed as the primary objects in such systems, with skyrmions being made out of them.

hep-th↗

arXiv2007

Large scale and large period limits of symmetric calorons

We construct SU(2) calorons, with non-trivial holonomy, instanton charge 2 and magnetic charge 0 or -1; these calorons have two constituent monopoles, with charges (2,2) or (2,1). Our calorons are U(1)-symmetric and are constructed via the Nahm transform. They fall into distinct families which can be classified using representation theory. We consider large scale and large period limits of these calorons; in particular, the large scale limit may be a monopole, or a caloron with different topological charges.

hep-th↗