Vortex solutions of Liouville equation and quasi spherical surfaces
Abstract
We identify the two-dimensional surfaces corresponding to certain solutions of the Liouville equation of importance for mathematical physics, the nontopological Chern-Simons (or Jackiw-Pi) vortex solutions, characterized by an integer N ≥ 1. Such surfaces, that we call S2(N), have positive constant Gaussian curvature, K, but are spheres only when N = 1. They have edges, and, for any fixed K, have maximal radius c that we find here to be c = N/K. If such surfaces are constructed in a laboratory by using graphene (or any other Dirac material), our findings could be of interest to realize table-top Dirac massless excitations on nontrivial backgrounds. We also briefly discuss the type of three-dimensional spacetimes obtained as the product S2(N) × &R;.
- Publication:
-
International Journal of Geometric Methods in Modern Physics
- Pub Date:
- 2020
- DOI:
- 10.1142/S0219887820501066
- arXiv:
- arXiv:2003.10902
- Bibcode:
- 2020IJGMM..1750106I
- Keywords:
-
- Geometry of two-dimensional surfaces;
- vortex solutions;
- graphene three-dimensional spacetimes;
- General Relativity and Quantum Cosmology;
- Condensed Matter - Other Condensed Matter;
- High Energy Physics - Theory;
- Mathematical Physics
- E-Print:
- 17 pages, 15 figures