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Spontaneously Broken $\bm{(-1)}$-Form U(1) Symmetries
by Daniel Aloni, Eduardo García-Valdecasas, Matthew Reece, Motoo Suzuki
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Eduardo Garcia Valdecasas · Matthew Reece |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202403_00019v2 (pdf) |
| Date submitted: | 2024-06-07 17:59 |
| Submitted by: | Garcia Valdecasas, Eduardo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Spontaneous breaking of symmetries leads to universal phenomena. We extend this notion to $(-1)$-form U(1) symmetries. The spontaneous breaking is diagnosed by a dependence of the vacuum energy on a constant background field $\theta$, which can be probed by the topological susceptibility. This leads to a reinterpretation of the Strong CP problem as arising from a spontaneously broken instantonic symmetry in QCD. We discuss how known solutions to the problem are unified in this framework and explore some, so far {\em unsuccessful}, attempts to find new solutions.
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
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
List of changes
1. We have changed F(X) to F(x).
2. We have specified the charge of the Dirac fermion above eq. 2.13.
3. The referee 1 asked about the dimensions of the compact boson phi. Indeed, it is dimensionless, but it is important to fix its normalization. We have assumed it to have period 2pi, which then requires us to fix the coefficient in front of its kinetic term. This constant is fixed by the bosonization dictionary for a boson that is dual to a free Dirac fermion. We have added footnote 10 clarifying this fact.
4. As the referee 1 noted, we introduced \epsilon without explaining its meaning. It is a UV regulator that is needed when bosonizing massive fermions. We have added an explanation below eq. 2.18.
5. The referee 1 is correct in pointing out that the symmetry of 2.13 is the same as the one as 2.14, including the (-1)-form symmetry. This is indeed the point of that discussion. We have modified the paragraph below eq. 2.13 to anticipate the fact that the (-1)-form symmetry is gauged in the Schwinger model. We hope this is enough to make the point clear. We have also added footnote 9 with the comment about fermion parity, which we have found insightful.
6. The referee 3 ask an interesting question regarding axions with potentials other than the one arising from QCD. We have added a paragraph at the end of section 4.1. explaining this case and its connection with the axion quality problem.
Current status:
Reports on this Submission
Report
The authors have addressed most of my comments but I am still confused by item 5 on the List of Changes. In the paragraph below (2.13), on the one hand, the authors state that " The symmetry of this theory is just U(1)_m^(−1)". On the other hand, in the same paragraph, they state "The explanation will be that the U(1)^(−1)_m symmetry has been gauged." I would kindly like to ask the authors to clarify if the (-1)-form symmetry is a global symmetry or a gauge symmetry of this theory.
Recommendation
Ask for minor revision
Author: Eduardo Garcia Valdecasas on 2024-06-11 [id 4557]
(in reply to Report 2 on 2024-06-07)The U(1)^(−1)_m symmetry is gauged. We have modified the paragraph below eq. 2.13 to be more clear about this fact.