A General Method for Transforming Nonphysical Configurations in BPS States

Abstract

In this work, we apply the so-called BPS method in order to obtain topological defects for a complex scalar field Lagrangian introduced by Trullinger and Subbaswamy. The BPS approach led us to compute new analytical solutions for this model.In our investigation, we found analytical configurations which satisfy the BPS first-order differential equations but do not obey the equations of motion of the model. Such defects were named non-physical ones. In order to recover the physical meaning of these defects, we proposed a procedure which can transform them into BPS states of new scalar field models. The new models here founded were applied in the context of hybrid cosmological scenarios, where we derived cosmological parameters compatible with the observed Universe. Such a methodology opens a new window to connect different two scalar fields systems and can be implemented in several distinct applications such as Bloch Branes, Lorentz and Symmetry Breaking Scenarios, Q-Balls, Oscillons, Cosmological Contexts, and Condensed Matter Systems.

Extended multi-scalar field theories in $$(1+1)$$ dimensions

“…Recently, there has been a great deal of interest in investigating multi-scalar field theories in (1 + 1) dimensions, which support kink solutions obeying first-order BPS equations [1][2][3][4][5][6][7]. Interesting applications have been found mainly in the context of cosmological models [8][9][10][11][12], in the study of some aspects of self-duality in generalised BPS theories [13][14][15], and also in connections with several others relevant subjects [16][17][18][19][20][21][22][23][24][25][26][27][28]. Among others topological defects [29,30], the study of kink solutions in scalar field theories are of great importance in several areas of the modern theoretical physics [31,32].…”