Quantum mass correction for the twisted kink

TL;DR

This paper derives an analytic expression for the quantum mass correction of the twisted  kink on S^1 using spectral zeta functions and Bethe ansatz, addressing renormalization and size optimization.

Contribution

It provides the first analytic calculation of the 1-loop quantum mass correction for the twisted  kink without explicit fluctuation spectrum knowledge.

Findings

Analytic expression for quantum mass correction derived

Renormalization issues discussed and addressed

Preferred size of the compact space identified

Abstract

We present an analytic result for the 1-loop quantum mass correction in semiclassical quantization for the twisted \phi^4 kink on S^1 without explicit knowledge of the fluctuation spectrum. For this purpose we use the contour integral representation of the spectral zeta function. By solving the Bethe ansatz equations for the n=2 Lame equation we obtain an analytic expression for the corresponding spectral discriminant. We discuss the renormalization issues of this model. An energetically preferred size for the compact space is finally obtained.