We investigate instantons on manifolds with Killing spinors and their cones. Examples of manifolds with Killing spinors include nearly Kähler 6-manifolds, nearly parallel G2-manifolds in dimension 7, Sasaki-Einstein manifolds, and 3-Sasakian manifolds. We construct a connection on the tangent bundle over these manifolds which solves the instanton equation, and also show that the instanton equation implies the Yang-Mills equation, despite the presence of torsion. We then construct instantons on the cones over these manifolds, and lift them to solutions of heterotic supergravity. Amongst our solutions are new instantons on even-dimensional Euclidean spaces, as well as the well-known BPST, quaternionic and octonionic instantons.

Nuclear binding energies are investigated in two variants of the Skyrme model: the first replaces the usual Skyrme term with a term that is sixth order in derivatives, and the second includes a potential that is quartic in the pion fields. Solitons in the first model are shown to deviate significantly from ans\"atze previously assumed in the literature. The binding energies obtained in both models are lower than those obtained from the standard Skyrme model, and those obtained in the second model are close to the experimental values.Comment: 22 pages, 11 figures v2: minor changes to text and one figur

We consider Lie(G)-valued G-invariant connections on bundles over spaces G/H, R×G/H and R 2 ×G/H, where G/H is a compact nearly Kähler six-dimensional homogeneous space, and the manifolds R×G/H and R 2 ×G/H carry G 2 -and Spin(7)-structures, respectively. By making a G-invariant ansatz, Yang-Mills theory with torsion on R×G/H is reduced to Newtonian mechanics of a particle moving in a plane with a quartic potential. For particular values of the torsion, we find explicit particle trajectories, which obey first-order gradient or hamiltonian flow equations. In two cases, these solutions correspond to anti-self-dual instantons associated with one of two G 2 -structures on R×G/H. It is shown that both G 2 -instanton equations can be obtained from a single Spin(7)-instanton equation on R 2 ×G/H.

A topological lower bound on the Skyrme energy which depends explicity on the pion mass is derived. This bound coincides with the previously best known bound when the pion mass vanishes, and improves on it whenever the pion mass is non-zero. The new bound can in particular circumstances be saturated. New energy bounds are also derived for the Skyrme model on a compact manifold, for the Faddeev-Skyrme model with a potential term, and for the Aratyn-Ferreira-Zimerman and Nicole models.

We discuss collapse and revival of Rabi oscillations in a system comprising a qubit and a "big spin" (made of N qubits, or spin-1/2 particles). We demonstrate a regime of behaviour analogous to conventional collapse and revival for a qubit-field system, employing spin coherent states for the initial state of the big spin. These dynamics can be used to create a cat state of the big spin. Even for relatively small values of N , states with significant potential for quantum metrology applications can result, giving sensitivity approaching the Heisenberg limit.

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 2monopole 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.

We consider a U(2) Yang-Mills theory on M × S 2 F where M is a Riemannian manifold and S 2 F is the fuzzy sphere. Using essentially the representation theory of SU(2) we determine the most general SU(2)-equivariant gauge field on M×S 2 F . This allows us to reduce the Yang-Mills theory on M × S 2 F 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 criticallycoupled abelian Higgs model in the commutative limit, S 2 F → 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.

The problem of constructing internally rotating solitons of fixed angular frequency ω in the Faddeev-Skyrme model is reformulated as a variational problem for an energylike functional, called pseudoenergy, which depends parametrically on ω. This problem is solved numerically using a gradient descent method, without imposing any spatial symmetries on the solitons, and the dependence of the solitons' energy on ω, and on their conserved total isospin J, studied. It is found that, generically, the shape of a soliton is independent of ω, and that its size grows monotonically with ω. A simple elastic rod model of time-dependent hopfions is developed which, despite having only one free parameter, accounts well for most of the numerical results.