Supersymmetric extensions of k-field models

Abstract

We investigate the supersymmetric extension of k-field models, in which the scalar field is described by generalized dynamics. We illustrate some results with models that support static solutions with the standard kink or the compact profile. PACS numbers: 11.30.Pb, 11.27.+d Topological defects may have important consequences in a diversity of contexts, in particular in Cosmology, where they appear very naturally through the presence of phase transitions in the early universe [1]. As it is well-known, one of the simplest structures, domain walls, spring from the breaking of discrete symmetry, guided by scalar fields, which will be the main focus of the present work. In this case, in models describing spontaneous breaking of some discrete symmetry, the presence of topological defects in canonical models of scalar fields with standard dynamics, the equations of motion are shown to reduce to firstorder differential equations, with the model being nothing but the bosonic portion of some more general supersymmetric theory. One usually refers to this possibility as the first-order framework, where the topological defects appear as solutions of first-order equations as BPS states, named after the pioneer investigations of Bogomol'nyi, and Prasad and Sommerfield [2].With the recent discovery that the universe is evolving through an accelerated expansion, models described by scalar fields with non-standard dynamics are being studied in the cosmological context, for instance, as the so-called k-fields, first introduced in the context of inflation [3] and then as k-essence models, suggested to solve the cosmic coincidence problem [4]. We recall that k-inflation [3] has appeared as a way to reconcile the string dilaton with inflation. However, as one knows, supersymmetry is supposed to be unbroken at high energies, so it may affect the inflationary evolution. In this sense, supersymmetric extensions of k-field dynamics seem to be of current interest to the physics at high energy scales.The case of scalar fields with standard dynamics has been studied in several different contexts, and here we point out a diversity of investigations on the presence of domain walls in supergravity theories -see, e.g., Ref.[5] and references therein. On the other hand, the presence of scalar field models with non-standard dynamics has stimulated several recent investigations, dealing with properties of topological structures in this new scenario [6][7][8][9][10][11][12]. The main issue here is to change the scalar field dynamics from the standard one

First-order formalism for twinlike models with several real scalar fields

“…A general feature of the generalized models is that they obey first-order differential equations, so a natural question to ask concerns the inclusion of fermions, to study if one can find supersymmetric extensions of the above models [17][18][19], to investigate the behavior of fermions under such generalized scenarios. This issue will be considered elsewhere.…”

“…It also shows that it is not a simple task to go explicitly to the first-order framework and find analytical solutions [16], an issue related to supersymmetry, to be considered elsewhere under the general guidance of Ref. [17][18][19]. The next step is then to deal with twinlike models, and this is done in Sec.…”

Extended supersymmetry and BPS solutions in baby Skyrme models

“…The investigation of SUSY extensions of genuinely nonstandard kinetic terms has been resumed only recently [55]- [63] (see also [64]- [67] for related discussions), where this rising interest is partly owed to the fact that field theories with non-standard kinetic terms may be instrumental in the resolution of some enigmas of cosmology [68]- [80]. Concretely, in [56] we demonstrated that the baby Skyrme model in the O(3) formulation does have a N = 1 SUSY extension for arbitrary non-negative potential.…”

Baby Skyrme model and fermionic zero modes

“…We can write (20) in a more suggestive way taking into account the on-shell solution for the auxiliary field (13) in the supersymmetric version of the model:…”

“…More recently in [16] and [17] the first N = 1 and N = 2 SUSY extensions of baby Skyrme models were constructed, in [18] the SUSY extension of the Faddeev-Skyrme model, in [22] the CP 1 Skyrme, and in [19] the SUSY extension of the Skyrme model. Supersymmetric extensions of general theories containing higher derivative terms were constructed in [20,21]. It is also interesting to note that the prototypical supersymmetric form of the N = 2 bS model has four dimensional analogues, e.g.…”