Minimal Model Renormalization Group Flows: Noninvertible Symmetries and Nonperturbative Description
Bibliographic record
Abstract
In this Letter we continue the investigation of RG flows between Virasoro minimal models of two-dimensional conformal field theories that are protected by noninvertible symmetries. RG flows leaving unbroken a subcategory of noninvertible symmetries are associated with anomaly matching conditions that we employ systematically to map the space of flows between minimal models beyond the Z_{2}-symmetric proposed recently in the literature. We introduce a family of nonlinear integral equations that appear to encode the exact finite-size, ground-state energies of these flows, including nonintegrable cases, such as the recently proposed M(kq+I,q)→M(kq-I,q). Our family of NLIEs encompasses and generalizes the integrable flows known in the literature: ϕ_{(1,3)}, ϕ_{(1,5)}, ϕ_{(1,2)} and ϕ_{(2,1)}. This work uncovers a new interplay between exact solvability and noninvertible symmetries. Furthermore, our nonperturbative description provides a nontrivial test for all the flows conjectured by anomaly matching conditions, but so far not observed by other means.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".