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Topological Data Analysis of Monopole Current Networks in $U(1)$ Lattice Gauge Theory
by Xavier Crean, Jeffrey Giansiracusa, Biagio Lucini
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Submission summary
| Authors (as registered SciPost users): | Xavier Crean · Jeffrey Giansiracusa · Biagio Lucini |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2403.07739v4 (pdf) |
| Code repository: | https://doi.org/10.5281/zenodo.10806185 |
| Data repository: | https://doi.org/10.5281/zenodo.10806046 |
| Date accepted: | 2024-09-13 |
| Date submitted: | 2024-08-30 11:54 |
| Submitted by: | Crean, Xavier |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
In $4$-dimensional pure compact $U(1)$ lattice gauge theory, we analyse topological aspects of the dynamics of monopoles across the deconfinement phase transition. We do this using tools from Topological Data Analysis (TDA). We demonstrate that observables constructed from the zeroth and first homology groups of monopole current networks may be used to quantitatively and robustly locate the critical inverse coupling $\beta_{c}$ through finite-size scaling. Our method provides a mathematically robust framework for the characterisation of topological invariants related to monopole currents, putting on firmer ground earlier investigations. Moreover, our approach can be generalised to the study of Abelian monopoles in non-Abelian gauge theories.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
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Author comments upon resubmission
Please accept the resubmission of our paper 'Topological Data Analysis of Monopole Current Networks in U(1) Lattice Gauge Theory'.
Yours sincerely,
The Authors
List of changes
Changes are in the format (1) brief summary of the referee request, (2) change that the authors have made.
1. Include sentence on the relation between chain complexes and graphs:
We have added a clarifying sentence to the start of Section 3.1.2.
2. Move Universal Coefficient Theorem to footnote:
The sentence about the Universal Coefficient Theorem has been moved to the footnote on page 9.
3. Replacement of term ‘stratification’ in Appendix B.3:
In Appendix B.3, in the main body of text, the term ‘stratification’ has been replaced by ‘finite partitioning’. A footnote has been added that mentions stratification for those readers who are familiar with the notion of a stratified space.
4. Correct typos:
Two typos were identified by a referee; these have been corrected.
5. Figures 4 and 6 use larger scatter symbols and curves to guide eye:
There are two changes we have made here. Firstly, for Figures 4 and 6, in the inset plots, we have increased the size of the markers and included the histogram reweighting curves used in the analysis. We believe this provides an appropriate visual guide. Note that reweighting windows have been suitably chosen to cover the peak of \chi_k points for each respective lattice size. Secondly, we have updated the captions for Figures 3, 4, 5 and 6 so that they all follow the same format of main plot description then inset plot description. The description of the plots has been updated to reflect the changes.
Published as SciPost Phys. 17, 100 (2024)