Kinks, Vortices and Monopoles

Supervisor: Daniele Dorigoni

Project IV, 2026-2027

Description:

This project is all about the study of solitons in various dimensions and understanding some of their peculiar properties. For example kinks (or domain walls) can be seen as waves travelling without any dissipation. Vortices are responsible for the draining of the water in your sink, and arise in a different guise in superconductors. Monopoles are the objects that you will never obtain by breaking a magnet in two! Between the possible topics:
  • Kinks solutions in two-dimensions, fermionic zero-modes and Derrick's theorem.
  • The Abrikosov-Nielsen-Olesen vortex, the motion and scattering of vortices.
  • The 't Hooft-Polyakov monopole. electro-magnetic duality of the Maxwell equations. Dyonic solutions.
  • Solitons in gauge theories.
and many other beautiful aspects of modern theoretical physics
Mode of Operation and Evidence of Learning: The project will revolve around learning through reading with focus on the underlying theory and the development of conceptual understanding. Students will demonstrate their understanding by exploring examples and theoretical applications of the material, and clearly communicating it in both written and oral formats. For programming inclined students there is the possibility of running simulations of vortices.
Prerequisites: 2H Methods of Mathematical Physics or equivalently Theoretical Physics II.
Useful but not necessary modules : 3H Solitons III and 4H Advanced quantum theory IV or equivalently the corresponding module in Physics. (Introduction to quantum fields)

Resources:

For some enjoyable introductory videos: For some reading material:

  • Topological solitons, N.Manton and P.Sutcliffe, CUP.
  • TASI lectures on solitons: Instantons, monopoles, vortices and kinks, D. Tong, hep-th/0509216 .
  • Aspects of symmetry, S. Coleman, CUP.

email: Daniele Dorigoni