Abstract
The Omega-deformation is a harmonic trap, penning certain excitations near the origin in a manner consistent with supersymmetry. Here we explore the dynamics of BPS monopoles and vortices in such a trap. We pay particular attention to monopoles in the Higgs phase, when they are confined to a vortex string. Unusually for BPS solitons, the mass of these confined monopoles is quadratic in the topological charges. We compute an index theorem to determine the number of collective coordinates of confined monopoles. Despite being restricted to move on a line, we find that they have a rich dynamics. As the strength of the trap increases, the number of collective coordinates can change, sometimes with constituent monopoles disappearing, sometimes with new ones emerging.
Highlights
The second motivation is more quantum in origin
We find that the presence of the harmonic trap endows these confined monopoles with a rich dynamics
The upshot is that, in the presence of the trap, only axially symmetric vortex configurations survive. We flesh out this statement in appendix A, where we show that the dynamics of vortices can be described as motion on the original moduli space in the presence of a potential
Summary
The theory of interest consists of a U(N ) gauge field Aμ, coupled to a real adjoint scalar φ and Nf fundamental scalars qi. We impose on these fields an external, harmonic trap whose strength is parameterised by ω. The Lagrangian (2.1) admits a number of different soliton solutions depending on the values of v2 and the real-valued masses mi.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
