Double vortex condensates in the Chern-Simons-Higgs theory

For a selfdual model introduced by Hong-Kim-Pac 18] and Jackiw-Weinberg 19] we study 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 with the existence of extremal functions for a Sobolev inequality of the Moser-Trudinger's type on the flat 2-torus (22], 1] and 15]). 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. Received: March 3, 1998 / Accepted October 23, 1998