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arXiv · 2404.16372

Conserved currents in five-dimensional proposals for lattice chiral gauge theories

Maarten Golterman·Yigal Shamir
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Abstract

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.

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Maarten Golterman, Yigal Shamir. 2024-04-25. Conserved currents in five-dimensional proposals for lattice chiral gauge theories. https://arxiv.org/abs/2404.16372

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