Domain walls without a potential

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 noncanonical 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.

Automated summary

Domain walls, or kinks, can be constructed in simple scalar theories without potential. These theories, belonging to a class of k-essence, show distinguishable characteristics through higher order perturbations or energy examination. The constructed domain walls are local, not global minima of the energy among field configurations with fixed topological charge.