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Quantum contribution to domain wall tension from spectral methods

N. Graham1 and H. Weigel2

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Phys. Rev. D 112, 045003 – Published 5 August, 2025

DOI: https://doi.org/10.1103/9v1m-rwjb

Abstract

In field theory, domain walls are constructed by embedding localized field configurations varying in one space dimension, such as the ϕ4 kink, in two or three space dimensions. At the classical level, the kink mass straightforwardly turns into the energy per unit length or area, known as the domain wall tension. The quantum contribution to the tension is more difficult to compute, because the quantum fluctuations about the domain wall in the additional coordinates must be included. We show that spectral methods, making use of scattering data for the interaction of quantum fluctuations with the domain wall background, are an efficient way to compute the leading quantum correction to the domain wall tension. In particular we demonstrate that within this approach it is straightforward to pass from one renormalization scheme to another.

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Phys. Rev. D 112, 045003– Published 5 August, 2025
  • Received 30 April 2025
  • Accepted 16 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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