A Remark on the Effective Description of Topological Defects

TL;DR

This paper critically reexamines the derivation of effective dynamics for topological defects, emphasizing the importance of correctly handling zero modes to avoid overcounting degrees of freedom, with implications for higher-dimensional defects.

Contribution

It highlights the necessity of proper gauge-fixing in deriving consistent effective actions for topological defects, addressing overlooked issues in recent literature.

Findings

Incorrect zero mode handling leads to inconsistent effective actions.

Proper gauge-fixing removes redundancy and ensures valid derivations.

Reevaluation of curvature corrections in light of the new approach.

Abstract

We subject the methodology used to derive the effective dynamics of topological defects to a critical reappraisal, using the two-dimensional kink as an illustrative example. Special care is taken on how the zero modes should be handled in order to avoid overcounting of degrees of freedom. This is an issue that has been overlooked in many recent contributions on the derivation of domain wall effective actions. We show that, unless such redundancy is completely removed by means of a sort of gauge-fixing, the expression obtained for the effective action will not be consistent. We readdress some earlier calculations over the existence of curvature corrections in the light of the previous discussion and briefly comment on the application of this method to higher dimensional topological defects.