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New field theories with foliation structure and subdimensional particles from the Godbillon-Vey invariant

Hiromi Ebisu1,*, Masazumi Honda2,†, Taiichi Nakanishi1,2,‡, and Soichiro Shimamori3,§

  • 1Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
  • 2Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN, Wako 351-0198, Japan
  • 3Department of Physics, Osaka University, Machikaneyama-Cho 1-1, Toyonaka 560-0043, Japan

  • *Contact author: hiromi.ebisu@yukawa.kyoto-u.ac.jp
  • †Contact author: masazumi.honda@riken.jp
  • ‡Contact author: taiichi.nakanishi@yukawa.kyoto-u.ac.jp
  • §Contact author: s_shimamori@het.phys.sci.osaka-u.ac.jp
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Phys. Rev. D 112, 025010 – Published 15 July, 2025

DOI: https://doi.org/10.1103/4fz5-9298

Abstract

Recently, subdimensional particles including fractons have attracted much attention from various areas. Notable features of such matter phases are mobility constraints and subextensive ground-state degeneracies (GSDs). In this paper, we propose a BF-like theory motivated by the Godbillon-Vey invariant, which is a mathematical invariant of the foliated manifold. Our theory hosts subsystem higher-form symmetries which manifestly ensure the mobility constraint and subextensive GSD through the spontaneous symmetry breaking. We also discuss some lattice spin models which realize the same low-energy behaviors as the BF-like theory. Furthermore, we explore dynamical matter theories which are coupled to the BF-like theory.

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Phys. Rev. D 112, 025010– Published 15 July, 2025
  • Received 22 March 2025
  • Accepted 13 May 2025
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