Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry

Journal Article · 01 February 2022 · SciPost Physics

DOI: https://doi.org/10.21468/SciPostPhys.12.2.050 · OSTI ID:1843272

Du, Yi-Hsien ^[1]; Mehta, Umang ^[1]; Nguyen, Dung ^[2]; Son, Dam Thanh ^[1]

---

1. University of Chicago
2. Brown University

We propose nonabelian higher-rank gauge theories in 2+1D and 3+1D. The gauge group is constructed from the volume-preserving diffeomorphisms of space. We show that the intriguing physics of the lowest Landau level (LLL) limit can be interpreted as the consequences of the symmetry. We derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term within our formalism. Using the gauge symmetry in 2+1D, we derive the LLL effective action of vortex crystal in rotating Bose gas as well as Wigner crystal of electron in an applied magnetic field. We show that the nonlinear sigma models of ferromagnets in 2+1D and 3+1D exhibit the higher-rank gauge symmetries that we introduce in this paper. We interpret the fractonic behavior of the excitations on the lowest Landau level and of skyrmions in ferromagnets as the consequence of the higher-rank gauge symmetry.

• Research Organization: Univ. of Chicago, IL (United States)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0009924
• OSTI ID: 1843272
• Journal Information: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 2 Vol. 12; ISSN 2542-4653
• Publisher: Stichting SciPostCopyright Statement
• Country of Publication: Netherlands
• Language: English