Abstract
We show that domain walls, or kinks, can be constructed in simple scalar theories where the scalar has no potential. These theories belong to a class of k-essence where the Lagrangian vanishes identically when one lets the derivatives of the scalar vanish. The domain walls we construct have positive energy and stable quadratic perturbations. As particular cases, we find families of theories with domain walls and their quadratic perturbations identical to the ones of the canonical Mexican hat or sine-Gordon scalar theories. We show that canonical and non canonical cases are nevertheless distinguishable via higher order perturbations or a careful examination of the energies. In particular, in contrast to the usual case, our walls are local minima of the energy among the field configuration having some fixed topological charge, but not global minima.
Highlights
Topological and nontopological solitons play an important role in various domains of physics ranging from liquid crystals, fluid mechanics to cosmology
Where the leftover terms are at least cubic in (x ∓ 1) and y. This shows that the domain wall solution represent a local minimum of the energy in the class of all field configuration having the same topological charge provided that the quantities Σκ;0 and Σκ;2 verify
We have shown in particular that domain walls can be supported by non-canonical kinetic terms only, without the help of a potential
Summary
Topological and nontopological solitons play an important role in various domains of physics ranging from liquid crystals, fluid mechanics to cosmology (see e.g., [1,2,3,4,5]). L 1⁄4 Pðφ; XÞ ð2Þ where the dependence of P on X and φ is nontrivial and in particular not given by a sum of a free kinetic energy X and potential energy VðφÞ Such theories have been considered in many instances and are usually denoted as k-essence in the context of cosmology and gravitation [6,7,8,9]. We introduce k-essence domain walls (Sec. III) and show how one can obtain kinks which have a profile just identical to the one of the canonical mexican hat model and discuss their stability and topological properties in a nonperturbative way. Two appendixes give technical details on some results introduced in the body of the text
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