Domain walls without a potential

TL;DR

This paper demonstrates the existence of stable domain walls in simple scalar theories without a potential, expanding the understanding of topological defects in non-standard field theories.

Contribution

It introduces a class of k-essence theories with zero Lagrangian at zero derivatives that support stable domain walls, differing from traditional potential-based models.

Findings

Domain walls with positive energy and stability are constructed without a potential.

Certain theories have domain walls identical to those in Mexican hat or sine-Gordon models.

These walls are local energy minima, not global, distinguishing them from canonical cases.

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.