Noninvertible anomalies in SU(N) × U(1) gauge theories
Bibliographic record
Abstract
Abstract We study 4-dimensional SU(N) × U(1) gauge theories with a single massless Dirac fermion in the 2-index symmetric/antisymmetric representations and show that they are endowed with a noninvertible 0-form $$ {\overset{\sim }{\mathbb{Z}}}_{2\left(N\pm 2\right)}^{\upchi} $$ ℤ ~ 2 N ± 2 χ chiral symmetry along with a 1-form $$ {\mathbb{Z}}_N^{(1)} $$ ℤ N 1 center symmetry. By using the Hamiltonian formalism and putting the theory on a spatial three-torus $$ \mathbbm{T} $$ T 3, we construct the non-unitary gauge invariant operator corresponding to $$ {\overset{\sim }{\mathbb{Z}}}_{2\left(N\pm 2\right)}^{\upchi} $$ ℤ ~ 2 N ± 2 χ and find that it acts nontrivially in sectors of the Hilbert space characterized by selected magnetic fluxes. When we subject $$ \mathbbm{T} $$ T 3 to $$ {\mathbb{Z}}_N^{(1)} $$ ℤ N 1 twists, for N even, in selected magnetic flux sectors, the algebra of $$ {\overset{\sim }{\mathbb{Z}}}_{2\left(N\pm 2\right)}^{\upchi} $$ ℤ ~ 2 N ± 2 χ and $$ {\mathbb{Z}}_N^{(1)} $$ ℤ N 1 fails to commute by a ℤ2 phase. We interpret this noncommutativity as a mixed anomaly between the noninvertible and the 1-form symmetries. The anomaly implies that all states in the torus Hilbert space with the selected magnetic fluxes exhibit a two-fold degeneracy for arbitrary $$ \mathbbm{T} $$ T 3 size. The degenerate states are labeled by discrete electric fluxes and are characterized by nonzero expectation values of condensates. In an appendix, we also discuss how to construct the corresponding noninvertible defect via the “half-space gauging” of a discrete one-form magnetic symmetry.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".