Abstract
We study kink (domain wall) solutions in a model consisting of two complex scalar fields coupled to two independent Abelian gauge fields in a Lagrangian that has U(1)×U(1) gauge plus Z2 discrete symmetry. We find consistent solutions such that while the U(1) symmetries of the fields are preserved while in their respective vacua, they are broken on the domain wall. The gauge field solutions show that the domain wall is sandwiched between domains with constant magnetic fields.
Highlights
These two vacua are degenerate and are the global minima of the potential for the parameter regime λ1 ≥ 0 and λ2 ≥ 0
Equation 4.3 shows that the currents are nonzero only when the gauge field configurations are nonzero and vice-versa, so these currents are responsible for dynamically generating the magnetic fields
In order to further explore the idea of the “clash of symmetries” from [4], we have considered a model in which two scalar fields are coupled to their respective gauge fields in a Lagrangian which has U (1) × U (1) symmetry
Summary
Using the the notation of [4] we start with the action for two complex scalar fields φ1,2 coupled to different U (1) gauge fields A1,2. We would like to construct domain wall solutions by requiring the scalar Higgs fields to asymptote to different respective vacua on either side of the wall. For a domain wall solution the scalar fields must obey the boundary conditions in eqn 2.7. [4]), if one takes symmetric (R1 + R2) and anti-symmetric (R1 − R2) linear combinations of the fields, the differential equations decouple for the special case of λ = 4 with analytic solutions, R1. This is not the case in our model for α = 0.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
