Avoid common mistakes on your manuscript.
Erratum to: Eur. Phys. J. C (2023) 83(6):481 https://doi.org/10.1140/epjc/s10052-023-11616-6
In this Erratum we do some corrections to equations in the continuum theory given in Sect. 2. Our discussions are falsely attributed to the \(2\pi \) periodicity of the compact scalar \(\chi \), and then the definition of the 4-form gauge field \(D^{(4)}\) is incorrect. These modifications do not modify any conclusion in the lattice theory.
A consistency check for the periodicity of the Lagrange multiplier \(\chi \) revealed that there was an error in the continuum Lagrangian. That is, Eq. (2.1) should be
Note that the third term in the right hand side is multiplied by q. Then, one can confirm the existence of the \(\mathbb {Z}_{pq}\) 3-form global symmetry.
Instead of Eq. (2.11), in order to maintain the periodicity of \(\chi \), we must impose the condition
The contribution from the quadratic term of \(B^{(2)}\) can in general take a value in \(\frac{1}{q}\mathbb {Z}\), but the other terms are integers. To admit of nontrivial configurations of \(B^{(2)}\), \(D^{(4)}\) (2.12) should be introduced as
where the 1-form transformation acts as
In particular, the \(2\pi \) periodicity of \(D^{(3)}\) is not violated by this gauge transformation. Therefore, Eq. (2.18) should be
The shift \(\theta \rightarrow \theta +2\pi /p\) gives rise to a \(\mathbb {Z}_{p q^2}\) phase:
Also, Eqs. (2.21) and (2.22) become
These modifications do not modify any conclusion in the lattice theory. We would like to thank Ryo Yokokura for valuable discussions. The authors would like to apologize for this error.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development.
About this article
Cite this article
Kan, N., Morikawa, O., Nagoya, Y. et al. Erratum to: Higher-group structure in lattice Abelian gauge theory under instanton-sum modification. Eur. Phys. J. C 84, 22 (2024). https://doi.org/10.1140/epjc/s10052-024-12386-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjc/s10052-024-12386-5