Non-invertible bosonic chiral symmetry on the lattice
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915565692518400 |
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| author | Fidkowski, Lukasz Xu, Cenke Zhang, Carolyn |
| author_facet | Fidkowski, Lukasz Xu, Cenke Zhang, Carolyn |
| contents | In this work we realize the 3 + 1 dimensional non-invertible ${\mathbb{Z}}_N$ chiral symmetry generator as an operator in a many body lattice Hilbert space. A crucial ingredient in our construction is the use of infinite dimensional $U(1)$ rotor site Hilbert spaces. Specifically, our Hilbert space is that of a $U(1)$ lattice gauge theory coupled to a charge $1$ scalar in the Villain formulation, which allows for direct access to monopoles and for a simple definition of a magnetic ${\mathbb{Z}}_N$ one-form symmetry $Z^{(1)}_m$ , at the lattice Hamiltonian level. We construct the generator of the ${\mathbb{Z}}_N$ chiral symmetry as as a unitary operator in the subspace of $Z^{(1)}_m$-invariant states, and show that it cannot be extended to the entire Hilbert space while preserving locality and unitarity. Using a lattice-level duality based on gauging $Z^{(1)}_m$, we find a dual description of this subspace, as the subspace of a charge $1/N$ gauge theory invariant under an electric one-form symmetry $Z^{(1)}_e$. We show that in this dual formulation, the chiral symmetry generator does extend unitarily to the entire Hilbert space, but has a mixed anomaly with the $Z^{(1)}_e$ symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17969 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-invertible bosonic chiral symmetry on the lattice Fidkowski, Lukasz Xu, Cenke Zhang, Carolyn Strongly Correlated Electrons High Energy Physics - Theory In this work we realize the 3 + 1 dimensional non-invertible ${\mathbb{Z}}_N$ chiral symmetry generator as an operator in a many body lattice Hilbert space. A crucial ingredient in our construction is the use of infinite dimensional $U(1)$ rotor site Hilbert spaces. Specifically, our Hilbert space is that of a $U(1)$ lattice gauge theory coupled to a charge $1$ scalar in the Villain formulation, which allows for direct access to monopoles and for a simple definition of a magnetic ${\mathbb{Z}}_N$ one-form symmetry $Z^{(1)}_m$ , at the lattice Hamiltonian level. We construct the generator of the ${\mathbb{Z}}_N$ chiral symmetry as as a unitary operator in the subspace of $Z^{(1)}_m$-invariant states, and show that it cannot be extended to the entire Hilbert space while preserving locality and unitarity. Using a lattice-level duality based on gauging $Z^{(1)}_m$, we find a dual description of this subspace, as the subspace of a charge $1/N$ gauge theory invariant under an electric one-form symmetry $Z^{(1)}_e$. We show that in this dual formulation, the chiral symmetry generator does extend unitarily to the entire Hilbert space, but has a mixed anomaly with the $Z^{(1)}_e$ symmetry. |
| title | Non-invertible bosonic chiral symmetry on the lattice |
| topic | Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2510.17969 |