On multivortex solutions in Chern-Simons gauge theory. (English) Zbl 0912.58046

Struwe, Michael; Tarantello, Gabriella

Boll. Unione Mat. Ital., Sez. B, Artic. Ric. Mat. (8) 1, No. 1, 109-121 (1998).

This work is motivated by the observation [see C. H. Taubes, Commun. Math. Phys. 72, 277-292 (1980; Zbl 0451.35101)] that certain self-dual equations for energy-minimizing multivortices in Chern-Simons theory can be reduced to suitable elliptic equations for the logarithmic value of the particle density. Here a particular class of elliptic equations arising in this way is considered on the 2-dimensional torus. The main result of the paper is an existence theorem for non-trivial solutions of the considered equations which is proven with the help of variational techniques.

Reviewer: V.Perlick (Berlin)

MSC:

58J90	Applications of PDEs on manifolds
58E30	Variational principles in infinite-dimensional spaces
81T13	Yang-Mills and other gauge theories in quantum field theory

Keywords:

self-dual equations; energy-minimizing multivortices; Chern-Simons theory; elliptic equations; two-dimensional torus

Citations:

Zbl 0451.35101