Bifundamental multiscalar fixed points in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn><mml:mo>−</mml:mo><mml:mi>ε</mml:mi></mml:math>
Bibliographic record
Abstract
We study fixed points of scalar fields that transform in the bifundamental representation of $O(N)\ifmmode\times\else\texttimes\fi{}O(M)$ in $3\ensuremath{-}\ensuremath{\epsilon}$ dimensions, generalizing the classic tricritical sextic vector model. In the limit where $N$ is large but $M$ is finite, we determine the complete beta function to order $1/N$ for arbitrary $M$. We find a rich collection of large-$N$ fixed points in $d=3$, as well as fixed points in $d=3\ensuremath{-}\ensuremath{\epsilon}$, that can be studied to all orders in the parameter $\stackrel{^}{\ensuremath{\epsilon}}=N\ensuremath{\epsilon}$. With the goal of defining a large-$N$ nonsupersymmetric conformal field theory dominated by a web of planar diagrams, we also study fixed points in the ``bifundamental'' large-$N$ limit, in which $M$ and $N$ are both large but the ratio $M/N$ is held fixed. We find a unique infrared fixed point in $d=3\ensuremath{-}\ensuremath{\epsilon}$, which we determine to order ${\ensuremath{\epsilon}}^{2}$. When $M/N\ensuremath{\ll}1$, we also find an ultraviolet fixed point in $d=3$ and $d=3\ensuremath{-}\ensuremath{\epsilon}$ that merges with the infrared fixed point at $\ensuremath{\epsilon}\ensuremath{\sim}O(M/N)$. We expect at least one of two candidate fixed points in integer dimensions---the infrared fixed point in $d=2$ and the ultraviolet fixed point in $d=3$---to survive for finite values of $M/N$.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.003 | 0.003 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.014 | 0.002 |
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".