Parametric representation of rank <i>d</i> tensorial group field theory: Abelian models with kinetic term ∑sps+μ
Bibliographic record
Abstract
We consider the parametric representation of the amplitudes of Abelian models in the so-called framework of rank d tensorial group field theory. These models are called Abelian because their fields live on copies of U(1)D. We concentrate on the case when these models are endowed with particular kinetic terms involving a linear power in momenta. A new dimensional regularization is introduced for particular models in this class: a rank 3 tensor model, an infinite tower of matrix models ϕ2n over U(1), and a matrix model over U(1)2. We prove that all divergent amplitudes are meromorphic functions in the complexified group dimension D ∈ ℂ. From this point, a standard subtraction program yielding analytic renormalized integrals could be applied. Furthermore, we identify and study in depth the Symanzik polynomials provided by the parametric amplitudes of generic rank d Abelian models. We find that these polynomials do not satisfy the ordinary Tutte’s rules (contraction/deletion). By scrutinizing the “face”-structure of these polynomials, we find a generalized polynomial which turns out to be stable only under contraction.
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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 | 0.001 | 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".