BPS Equations of Monopole and Dyon in SU(2)‎ Yang-Mills-Higgs Model, Nakamula-Shiraishi Models, and Their Generalized Versions from the BPS Lagrangian Method

Abstract EN

We apply the BPS Lagrangian method to derive BPS equations of monopole and dyon in the SU2 Yang-Mills-Higgs model, Nakamula-Shiraishi models, and their generalized versions.

We argue that, by identifying the effective fields of scalar field, f, and of time-component gauge field, j, explicitly by j=βf with β being a real constant, the usual BPS equations for dyon can be obtained naturally.

We validate this identification by showing that both Euler-Lagrange equations for f and j are identical in the BPS limit.

The value of β is bounded to β<1 due to reality condition on the resulting BPS equations.

In the Born-Infeld type of actions, namely, Nakamula-Shiraishi models and their generalized versions, we find a new feature that, by adding infinitesimally the energy density up to a constant 4b2, with b being the Born-Infeld parameter, it might turn monopole (dyon) to antimonopole (antidyon) and vice versa.

In all generalized versions there are additional constraint equations that relate the scalar-dependent couplings of scalar and of gauge kinetic terms or G and w, respectively.

For monopole the constraint equation is G=w-1, while for dyon it is wG-β2w=1-β2 which further gives lower bound to G as such G≥2β1-β2.

We also write down the complete square-forms of all effective Lagrangians.