Scalar fields with impurities in arbitrary dimensions: first-order framework and exact solutions

TL;DR

This paper develops a first-order framework for scalar fields with impurities in any dimension, enabling exact solutions and stability analysis, advancing understanding of impurity effects in scalar field models.

Contribution

It introduces a novel first-order differential equation approach for scalar fields with impurities, allowing exact solutions in arbitrary dimensions.

Findings

Exact solutions are obtainable via the first-order equation.

The energy density can be expressed as a divergence of an auxiliary vector.

Stability under rescaling is analyzed for various models.

Abstract

We study a class of scalar field models coupled to impurities in arbitrary spacetime dimensions. The system admits the introduction of a second-order tensor that can be forced to obey an equality, if a first-order differential equation is satisfied, compatible with the equation of motion when the potential engenders a very specific form. In the case of static solutions, the energy density of the system can equal the divergence of an auxiliary vector function, which is included to help us solve the model. Stability of the field configuration under rescale of argument is investigated, and the procedure is illustrated considering distinct canonical models. The results show that exact solutions can be obtained in arbitrary dimensions, related to the presence of the first-order equation.