More on bogomol’nyi equations of three-dimensional generalized maxwell-higgs model using on-shell method

Abstract

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 C0 and they can be classified into two types determined by the value of C0 = 0 and C0 ≠ 0. We identify that the Bogomol’nyi equations obtained by Bazeia et al. [2] are of the (C0 = 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 (C0 ≠ 0)-type Bogomol’nyi equations. This non-zero C0 is related to a non-trivial function fC0 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 P remain zero globally by the finite energy constraint.