Anomaly-free symmetries with obstructions to gauging and onsiteability

• URL: http://arxiv.org/abs/2507.21267v1
• Date: Mon, 28 Jul 2025 18:48:39 GMT
• Title: Anomaly-free symmetries with obstructions to gauging and onsiteability
• Authors: Wilbur Shirley, Carolyn Zhang, Wenjie Ji, Michael Levin,
• Abstract summary: We present counterexamples to the lore that symmetries that cannot be gauged or made on-site are necessarily anomalous.<n>Specifically, we construct unitary, internal symmetries of two-dimensional lattice models that cannot be consistently coupled to background or dynamical gauge fields.<n>These symmetries are nevertheless anomaly-free in the sense that they admit symmetric, gapped Hamiltonians with unique, invertible ground states.
• Score: 0.35998666903987897
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present counterexamples to the lore that symmetries that cannot be gauged or made on-site are necessarily anomalous. Specifically, we construct unitary, internal symmetries of two-dimensional lattice models that cannot be consistently coupled to background or dynamical gauge fields or disentangled to a tensor product of on-site operators. These symmetries are nevertheless anomaly-free in the sense that they admit symmetric, gapped Hamiltonians with unique, invertible ground states. We show that symmetries of this kind are characterized by an index $[\omega]\in H^2(G,\mathbb{Q}_+)$, where $\mathbb{Q}_+$ is the multiplicative group of rational numbers labeling one-dimensional quantum cellular automata.

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