Double vortex condensates in the Chern-Simons-Higgs theory. (English) Zbl 0951.58030

Nolasco, Margherita; Tarantello, Gabriella

Calc. Var. Partial Differ. Equ. 9, No. 1, 31-94 (1999).

Summary: For a selfdual model introduced by J. Hong, Y. Kim and P. Pac and R. Jackiw and E. Weinberg we studye the existence of double vortex-condensates “bifurcating” from the symmetric vacuum state as the Chern-Simons coupling parameter \(k\) tends to zero. Surprisingly, we show a connection between the asymptotic behavior of the given double vortex as \(k\to 0^+\) with the existence of extremal functions for a Sobolev inequality of the Moser-Trudinger type on the flat 2-torus. In fact, our construction yields to a “best” minimizing sequence for the (non-coercive) associated extremal problem, in the sense that, the infimum is attained if and only if the given minimizing sequence admits a convergent subsequence.

MSC:

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

Keywords:

Chern-Simons-Higgs theory; double vortex-condensates