BPS VORTICES IN THE GENERALIZED MAXWELL-CHERN-SIMONS-HIGGS MODEL

• Main Author: Yudha Prasetya Tama, Laurenzius
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/67124
• Institution: Institut Teknologi Bandung

In field theory, soliton is known as the classical solution of a nonlinear model with topological structure that is different from its vacuum. In 2 + 1 dimensional spacetime, there exist a kind of soliton with codimension two that is called vortex. This soliton is symmetric under U(1) transformation group, locally and globally. Vortices with local U(1) transformation have gauge field added into its Lagrangian. The standard kinetic term to the gauge field is the Maxwell Lagrangian. However, in planar dimension there exist another possible term which may describe the kinetic of the gauge field, namely the Chern-Simons term. Chern-Simons terms is gauge invariant up to the boundary term. These type of solitons can be described by first order differential equations which minimize the energy and satisfy the Euler-Lagrange equations. Those equations are known as the Bogomol’nyiPrasad-Sommerfield (BPS) equations. To obtain BPS equations, in this thesis we implement the BPS Lagrangian method. In particular, the BPS Lagrangian that is used consists of first derivative of the fields of degree one and without crossing terms. The model that is analyzed in this model is BPS vortices with the kinetic terms of the gauge field being described by both Maxwell and Chern-Simons term and coupled to the Higgs field (MCSH). The model is being generalized by adding positive-definite and dimensionless coupling functions which depend on the scalar fields. Upon analysis of the BPS limit, we conclude that the vortex solution may exist in the generalized MCSH model, with all of the involved fields are independent to one another, if the temporal gauge field has a constant value. In this thesis, we consider two cases namely BPS vortices with nonconstant neutral scalar field, and constant neutral scalar field. For the former case, we obtain vortex solution that satisfy finite energy condition under the standard boundary condition for the topological vortices upon introducing some particular generalized coupling functions. These BPS vortices differ from the known vortex solutions, that the BPS vortices have no electric field and yet they have nonzero magnetic charge. In case of constant neutral scalar field, the obtained solution is identical to the MCSH model without neutral scalar field where we set the temporal gauge field to be nonzero constant. The numerical solution of this model is also similar to the case of nonconstant neutral scalar field. It has magnetic charge and the energy density is zero near its origin.