More on Bogomol’nyi equations of three-dimensional generalized Maxwell-Higgs model using on-shell method

We use a recent on-shell method, developed in [1], to construct bogomol’nyi equations of the three-dimensional generalized maxwell-higgs model [2]. the resulting bogomol’nyi equations are parametrized by a constant c 0 and they can be classified into two types determined by the value of c 0 = 0 and c 0 ≠ 0. we identify that the bogomol’nyi equations obtained by bazeia et al. [2] are of the (c 0 = 0)-type bogomol’nyi equations. we show that the bogomol’nyi equations of this type do not admit the prasad-sommerfield limit in its spectrum. as a resolution, the vacuum energy must be lifted up by adding some constant to the potential. some possible solutions whose energy equal to the vacuum are discussed briefly. the on-shell method also reveals a new (c 0 ≠ 0)-type bogomol’nyi equations. this non-zero c 0 is related to a non-trivial function $$ {f}_{{mathrm{c}}_0} $$ defined as a difference between energy density of the scalar potential term and of the gauge kinetic term. it turns out that these bogomol’nyi equations correspond to vortices with locally non-zero pressures, while their average pressure $$ mathcal{p} $$ remain zero globally by the finite energy constraint.