Conserved currents in five-dimensional proposals for lattice chiral gauge theories
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916282330251264 |
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| author | Golterman, Maarten Shamir, Yigal |
| author_facet | Golterman, Maarten Shamir, Yigal |
| contents | We apply the Grabowska-Kaplan framework, originally proposed for lattice chiral gauge theories, to QCD. We show that the resulting theory contains a conserved and gauge invariant singlet axial current, both on the lattice and in the continuum limit. This must give rise to a difference with QCD, with the simplest possibility being a superfluous Nambu-Goldstone boson in the physical spectrum not present in QCD. We find a similar unwanted conserved current in the recent "disk" formalism [Kaplan, Kaplan & Sen], this time limiting ourselves to the continuum formulation. A similar problem is expected when either of these formalisms is used for its original goal of constructing lattice chiral gauge theories. Finally we discuss a conjecture about the possible dynamics that might be associated with the unwanted conserved current, and the fate of 't Hooft vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16372 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conserved currents in five-dimensional proposals for lattice chiral gauge theories Golterman, Maarten Shamir, Yigal High Energy Physics - Lattice High Energy Physics - Theory We apply the Grabowska-Kaplan framework, originally proposed for lattice chiral gauge theories, to QCD. We show that the resulting theory contains a conserved and gauge invariant singlet axial current, both on the lattice and in the continuum limit. This must give rise to a difference with QCD, with the simplest possibility being a superfluous Nambu-Goldstone boson in the physical spectrum not present in QCD. We find a similar unwanted conserved current in the recent "disk" formalism [Kaplan, Kaplan & Sen], this time limiting ourselves to the continuum formulation. A similar problem is expected when either of these formalisms is used for its original goal of constructing lattice chiral gauge theories. Finally we discuss a conjecture about the possible dynamics that might be associated with the unwanted conserved current, and the fate of 't Hooft vertices. |
| title | Conserved currents in five-dimensional proposals for lattice chiral gauge theories |
| topic | High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.16372 |