We prove that the equations of motion describing domain walls in a Wess-Zumino theory involving only one chiral matter multiplet can be factorized into first order Bogomol'nyi equations, so that all the topological defects are of the Bogomol'nyi-Prasad-Sommerfield type.
We investigate bosonic sectors of supersymmetric field theories. We consider superpotentials described by one and by two real scalar fields, and we show how the equations of motion can be factorized into a family of first order Bogomol'nyi equations, so that all the topological defects are of the Bogomol'nyi-Prasad-Sommerfield type. We examine explicit models, that engender the ZN symmetry, and we identify all the topological sectors, illustrating their integrability.PACS numbers: 11.27.+d, 11.30.Pb, 11.30.Er Domain walls are defect structures that appear in diverse branches of physics. They usually live in three spatial dimensions as bidimensional objects that arise in systems described by potentials that contain at least two isolated degenerate minima. They involve energy scales as different as the ones that appear in Condensed Matter [1] and in Cosmology [2].A lot of attention has been drawn recently to domain walls in field theories, in models that have been investigated under several distinct motivations [3][4][5][6][7][8][9][10][11][12][13][14][15]. A very specific motivation concerns the presence of domain walls arising in between non zero vacuum expectation values of scalar fields in supergravity [5,6]. Another line deals with the formation of defects inside domain walls [7][8][9]. A great deal of attention has also been drawn to SU (N ) supersymmetric gluodynamics, where nonperturbative effects give rise to gluino condensates that may form according to a set of N isolated degenerate chirally asymmetric vacua, from where domain walls spring interpolating between pairs of vacua [10].The interest in domain walls in general widens because of the interplay between Field Theory and the low energy world volume dynamics of branes in String Theory [16][17][18][19]. In the case of intersection of defects, in particular in Ref.[12] some aspects of wall junctions have been investigated when the discrete symmetry is the Z N symmetry, in systems described by a single complex field, with the superpotentialThe second work in Ref.[12] has shown that the tensions of the topological defects that appear in these systems can be cast to the formwhere [N/2] is the biggest integer not bigger than N/2 itself. In Ref.[3] the same result was obtained, in an investigation concerned with exact integrability, due to the presence of infinitely many conserved currents -see also Ref.[20] for other investigations, in particular on the explicit form of the BPS solutions at large N.In the present work we examine the bosonic portion of supersymmetric theories, similar to the above models, that are of general interest to supersymmetry. Our investigations follow the lines of the former work [15], and bring new results on the presence of domain defects in models described by one and two real scalar fields. We start investigating systems with a single real scalar field. We write the Lagrangian density in the standard formis the superpotential, and W φ = dW/dφ. We search for defect structures, for static solutions of the equation of motion. ...
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