Global dipole symmetry, compact Lifshitz theory, tensor gauge theory, and fractons

Gorantla, Pranay; Lam, Ho Tat; Seiberg, Nathan; Shao, Shu-Heng

doi:10.1103/physrevb.106.045112

Title: Global dipole symmetry, compact Lifshitz theory, tensor gauge theory, and fractons

Journal Article · 11 July 2022 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.106.045112 · OSTI ID:1879853

^[1]; Lam, Ho Tat ^[2]; Seiberg, Nathan ^[3];

^[4]

Princeton Univ., NJ (United States); Institute for Advanced Study
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Institute for Advanced Study, Princeton, NJ (United States)
Stony Brook Univ., NY (United States)

We study field theories with global dipole symmetries and gauge dipole symmetries. The famous Lifshitz theory is an example of a theory with a global dipole symmetry. We study in detail its 1+1d version with a compact field. When this global symmetry is promoted to a $U(1)$ dipole gauge symmetry, the corresponding gauge field is a tensor gauge field. This theory is known to lead to fractons. In order to resolve various subtleties in the precise meaning of these global or gauge symmetries, we place these 1+1d theories on a lattice and then take the continuum limit. Interestingly, the continuum limit is not unique. Different limits lead to different continuum theories, whose operators, defects, global symmetries, etc. are different. We also consider a lattice gauge theory with a $$\mathbb Z_N$$ dipole gauge group. Surprisingly, several physical observables, such as the ground state degeneracy and the mobility of defects depend sensitively on the number of sites in the lattice. Our analysis forces us to think carefully about global symmetries that do not act on the standard Hilbert space of the theory, but only on the Hilbert space in the presence of defects. We refer to them as time-like global symmetries and discuss them in detail. Furthermore, these time-like global symmetries allow us to phrase the mobility restrictions of defects (including those of fractons) as a consequence of a global symmetry.

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Research Organization:: Institute for Advanced Study, Princeton, NJ (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0009988

OSTI ID:: 1879853

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 4 Vol. 106; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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