On multivortices in the electroweak theory II: Existence of Bogomol'nyi solutions in ℝ2

Solitons in Field Theory and Nonlinear Analysis

“…A common feature is that in both situations the solutions are minimizers of the energy functional and fluxes are quantized. Another is that the conditions for existence are independent of the locations of vortices but only depending on the total topological charge or the vortex number N. In the full plane setting, the former does not allow the existence of finite-energy Bogomol'nyi type vortices [293]. In order to get finite-energy solutions, it is important to put into consideration the effect of gravity through the coupling of the Einstein equations [348].…”

Selfdual Maxwell-Chern-Simons Vortices

“…We also recall [49] and [36] for other interesting results about Liouville's systems. Concerning self-dual electroweak vortices, we mention the work in [120], [27] and [28] in the planar case, and [119], [11] in the periodic case where sharp existence results are established for vortex number N = 1, 2, 3, 4. The analysis of the case N > 4 is still incomplete and in this direction a first contribution is contained in [9] that aims to extend the analysis of [43], [44] to "singular" Liouville-type equations in presence of Dirac measures.…”

Mean Field Equation of Liouville Type with Singular Data: Topological Degree

“…Chern-Simons-Higgs theory (see Hong-Kim-Pac [28] and Jackiw-Weinberg [29]) and to the electroweak theory (see Ambjorn-Olesen [5]). For the recent mathematical development, we refer the readers to Nolasco-Tarantello [42][43][44], Spruck-Yang [48][49][50], Tarantello [54], and Yang [57]. See also [7, 12, 15, 21, 24-26, 30, 39, 40].…”