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Landau theory for lattice higher-form gauge theories and the Kramers-Wannier duality

Kiyoharu Kawana*

  • *Contact author: kkiyoharu@kias.re.kr
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Phys. Rev. D 112, 074514 – Published 27 October, 2025

DOI: https://doi.org/10.1103/ftcr-m4mr

Abstract

We derive a Landau field theory for a lattice higher gauge theory defined on p-dimensional open cells (i.e., sites, links, faces, cubes, etc.), and study its continuum-limit and phases. In this approach, the p-dimensional Wilson-surface operator of the higher gauge theory is promoted to a fundamental functional field that is charged under the p-form global symmetry. By explicitly solving the functional equation of motion, we show that the classical solution exhibits the area (perimeter) law in the strong (weak) gauge coupling limit. In the deconfined phase, we also construct topological defects for both U(1) and ZN higher-form gauge theories, as analogs of vortex and domain-wall solutions in conventional field theories with 0-form global symmetries. Besides, we examine low-energy effective theory by identifying the phase modulations of the functional field as low-energy modes, and discuss the Coleman-Mermin-Wagner theorem for higher-form global symmetries. Finally, we discuss infrared duality among Landau field theories, which originates from Kramers-Wannier duality in lattice higher-form gauge theories.

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Phys. Rev. D 112, 074514– Published 27 October, 2025
  • Received 25 July 2025
  • Accepted 10 October 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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