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A symmetry principle for gauge theories with fractons

by Yuji Hirono, Minyoung You, Stephen Angus, Gil Young Cho

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Submission summary

Authors (as registered SciPost users): Yuji Hirono
Submission information
Preprint Link:  (pdf)
Date accepted: 2024-02-01
Date submitted: 2023-11-28 18:57
Submitted by: Hirono, Yuji
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
Approach: Theoretical


Fractonic phases are new phases of matter that host excitations with restricted mobility. We show that a certain class of gapless fractonic phases are realized as a result of spontaneous breaking of continuous higher-form symmetries whose conserved charges do not commute with spatial translations. We refer to such symmetries as nonuniform higher-form symmetries. These symmetries fall within the standard definition of higher-form symmetries in quantum field theory, and the corresponding symmetry generators are topological. Worldlines of particles are regarded as the charged objects of 1-form symmetries, and mobility restrictions can be implemented by introducing additional 1-form symmetries whose generators do not commute with spatial translations. These features are realized by effective field theories associated with spontaneously broken nonuniform 1-form symmetries. At low energies, the theories reduce to known higher-rank gauge theories such as scalar/vector charge gauge theories, and the gapless excitations in these theories are interpreted as Nambu--Goldstone modes for higher-form symmetries. Due to the nonuniformity of the symmetry, some of the modes acquire a gap, which is the higher-form analogue of the inverse Higgs mechanism of spacetime symmetries. The gauge theories have emergent nonuniform magnetic symmetries, and some of the magnetic monopoles become fractonic. We identify the 't~Hooft anomalies of the nonuniform higher-form symmetries and the corresponding bulk symmetry-protected topological phases. By this method, the mobility restrictions are fully determined by the choice of the commutation relations of charges with translations. This approach allows us to view existing (gapless) fracton models such as the scalar/vector charge gauge theories and their variants from a unified perspective and enables us to engineer theories with desired mobility restrictions.

Author comments upon resubmission

Dear Editor,

We thank the reviewers for the careful reading of the manuscript and the helpful feedback. In response to the reviewers' comments, we have updated out manuscript. Our responses to both reviewers can be found in the reply to the reports.

Yuji Hirono, Minyoung You, Stephen Angus, and Gil Young Cho

List of changes

- We added a new appendix titled "Coupling to complex scalar fields" as Appendix A in which we discussed the coupling of gauge fields of non-uniform symmetries to a theory with a complex scalar field.

- We added a new footnote on page 4 in which we comment on the case of curved spacetime.

- We have fixed a typo in Eq. (56) of the previous manuscript (Eq. (57) in the updated one).

- We have added a new comment in Summary and Discussions (the second point in the list of possible future directions on page 37).

- We have replaced the phrasing "has non-vanishing commutation relations with translations," with "can be written as a commutator of a translation and another charge" on page 6 and page 22.

- We have Footnote 3 on page 6 with the following content:
"We will use the same symbol $Q$ to denote the charge of a 0-form symmetry and the charge of the corresponding 1-form symmetry that appears as a result of the gauging of the former, to emphasize the connection between these two symmetries. When we wish to highlight the degree of the symmetry, we explicitly write the dependence on the underlying manifold over which the charge density is integrated, e.g. $Q(V)$ and $Q(S)$, where $V$ and $S$ are a $d$-cycle and a $(d-1)$-cycle, respectively."

- We have corrected Eq. (191), and we have modified the discussion prior to Eq. (191). We have also added footnote 21 following Eq. (192) to clarify our conventions.

- We have replaced Eq. (249), fixed Eqs. (250) and (269), and modified the surrounding arguments.

- We added a derivation of the equations of motion of the scalar charge gauge theory from the equations of motion (53)-(56) in page 12 (see around Eq. (69)-(76)).

Published as SciPost Phys. 16, 050 (2024)

Reports on this Submission

Anonymous Report 1 on 2023-12-18 (Invited Report)


The authors have answered in detail the points raised in the previous report. They have corrected some minor issues that do not affect to their results and have extended their analysis to include additional matter fields. In my opinion the paper can be published without further changes.

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