BPS VORTEKS IN THE GENERALIZED MAXWELL-CHERN-SIMONS-HIGGS MODEL IN 1+ 2 DIMENSIONS - Yudha Prasetya Tama, Laurenzius
Vortex is a two-dimensional soliton with finite core size. In this final project, we analyze the vortex solution of the generalized Maxwell-Chern-Simons-Higgs (MCSH) model using the BPS Lagrangian method. In the first part, we consider the generalized MCSH model that was introduced in Ref. [1]. Using the radially symmetric ansatz, we define the BPS Lagrangian with non-boundary terms containing zeroth order of the first-derivative of effective fields and quadratic terms of the first-order derivative for N and A0 field. From this, we can obtain the BPS equations for a(r) and g(r) rigorously. The governing equation for N and A0 is obtained as an additional constraint equation derived as the Euler-Lagrange equation of the BPS Lagrangian. There is another possible identification for the effective field N and A0 that is A0 = N from the remaining constrain equation. For this possibility, we analyze the numerical solution. From the obtained numerical result, we can say that this identification corresponds to the negative electric charge of the vortex. We also show that the plus and minus sign in the BPS equation is related to the magnetic charge of a vortex. For the second part, we consider the generalized MCSH model without a neutral scalar field, N. In this model, we define BPS Lagrangian with the non-boundary term only consist of the zeroth-order of the first derivative of a field. We obtain the BPS equation for each effective field with the BPS equation for the scalar gauge field is A0 = k0 with k0 being a real positive definite constant such that the obtained result can the regarded as an electrically neutral vortex solution. The stability of this solution is analyzed via finite energy condition which gives EBPS = 2pk0n from which can be concluded that this solution is, in fact, stable.