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Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum

by Tomas Brauner, Naoki Yamamoto, Ryo Yokokura

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Submission summary

Authors (as registered SciPost users): Tomas Brauner
Submission information
Preprint Link:  (pdf)
Date accepted: 2024-02-05
Date submitted: 2024-01-26 08:55
Submitted by: Brauner, Tomas
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
Approach: Theoretical


We demonstrate the general existence of a local dipole conservation law in bosonic field theory. The scalar charge density arises from the symplectic form of the system, whereas the tensor current descends from its stress tensor. The algebra of spatial translations becomes centrally extended in presence of field configurations with a finite nonzero charge. Furthermore, when the symplectic form is closed but not exact, the system may, surprisingly, lack a well-defined momentum density. This leads to a theorem for the presence of additional light modes in the system whenever the short-distance physics is governed by a translationally invariant local field theory. We also illustrate this mechanism for axion electrodynamics as an example of a system with Nambu-Goldstone modes of higher-form symmetries.

Author comments upon resubmission

We have addressed the point raised by the second referee in their report, and hope that the revised manuscript can be accepted for publication.

The Authors

List of changes

We have expanded the last paragraph of Sec. 5 to stress the novelty of our results concerning dipole symmetries. In addition, we have rewritten the paragraph below Eq. (60). Other than that, we have only updated references [4] and [11] with publication data.

Published as SciPost Phys. 16, 051 (2024)

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