Comment on thickness-corrections to Nambu-wall

TL;DR

This paper clarifies the finite-thickness corrections to the Nambu action for curved domain walls, showing no first order but a second order correction related to Ricci curvature, through consistent expansion methods.

Contribution

It provides a corrected analysis of thickness corrections, disputing previous claims and identifying a specific second order correction term.

Findings

No first order thickness corrections found.

A second order correction proportional to Ricci curvature identified.

Results obtained through consistent expansion of the action and equations of motion.

Abstract

We comment on some calculations concerning the finite-thickness corrections to the (generalized) Nambu action for a curved domain wall in Minkowski space. Contrary to a recent claim in the literature, we find no first order corrections in the wall-thickness, and only one second order correction proportional to the Ricci curvature of the wall. These results are obtained by consistently expanding the action and the equations of motion for the scalar field.