Higher-Form Anomalies on Lattices
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908789683257344 |
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| author | Feng, Yitao Kobayashi, Ryohei Chen, Yu-An Ryu, Shinsei |
| author_facet | Feng, Yitao Kobayashi, Ryohei Chen, Yu-An Ryu, Shinsei |
| contents | Higher-form symmetry in a tensor product Hilbert space is always emergent: the symmetry generators become genuinely topological only when the Gauss law is energetically enforced at low energies. In this paper, we present a general method for defining the 't Hooft anomaly of higher-form symmetries in lattice models built on a tensor product Hilbert space. In (2+1)D, for given Gauss law operators realized by finite-depth circuits that generate a finite 1-form $G$ symmetry, we construct an index representing a cohomology class in $H^4(B^2G, U(1))$, which characterizes the corresponding 't Hooft anomaly. This construction generalizes the Else-Nayak characterization of 0-form symmetry anomalies. More broadly, under the assumption of a specified formulation of the $p$-form $G$ symmetry action and Hilbert space structure in arbitrary $d$ spatial dimensions, we show how to characterize the 't Hooft anomaly of the symmetry action by an index valued in $H^{d+2}(B^{p+1}G, U(1))$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_12304 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-Form Anomalies on Lattices Feng, Yitao Kobayashi, Ryohei Chen, Yu-An Ryu, Shinsei Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Quantum Physics Higher-form symmetry in a tensor product Hilbert space is always emergent: the symmetry generators become genuinely topological only when the Gauss law is energetically enforced at low energies. In this paper, we present a general method for defining the 't Hooft anomaly of higher-form symmetries in lattice models built on a tensor product Hilbert space. In (2+1)D, for given Gauss law operators realized by finite-depth circuits that generate a finite 1-form $G$ symmetry, we construct an index representing a cohomology class in $H^4(B^2G, U(1))$, which characterizes the corresponding 't Hooft anomaly. This construction generalizes the Else-Nayak characterization of 0-form symmetry anomalies. More broadly, under the assumption of a specified formulation of the $p$-form $G$ symmetry action and Hilbert space structure in arbitrary $d$ spatial dimensions, we show how to characterize the 't Hooft anomaly of the symmetry action by an index valued in $H^{d+2}(B^{p+1}G, U(1))$. |
| title | Higher-Form Anomalies on Lattices |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2509.12304 |