Comment on "Continuum dual theory of the transition in 3D lattice superconductor"

TL;DR

This paper critiques a recent study on 3D lattice superconductors, identifying an inconsistency that challenges its conclusion about the divergence of magnetic penetration depth and its associated critical exponent.

Contribution

It exposes an internal inconsistency in Herbut's paper, questioning the validity of its main conclusion regarding the critical behavior of the magnetic penetration depth.

Findings

Identifies an inconsistency in Herbut's argument.

Challenges the conclusion about XY-exponent divergence.

Supports previous mean-field exponent predictions.

Abstract

A recent paper by Herbut in J. Phys. A: Math. Gen. {\bf 29}, 1 (1996) is shown to contain an internal inconsistency which invalidates the principal conclusion of the paper that the magnetic penetration depth diverges with an XY-exponent rather than a mean-field exponent, as predicted some time ago by Kiometzis, Kleinert, and Schakel (KKS).