Gross-Neveu-Yukawa theory of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>SO</mml:mi> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mi>N</mml:mi> <mml:mo>)</mml:mo> <mml:mo>→</mml:mo> <mml:mi>SO</mml:mi> <mml:mo>(</mml:mo> <mml:mi>N</mml:mi> <mml:mo>)</mml:mo> <mml:mo>×</mml:mo> <mml:mi>SO</mml:mi> <mml:mo>(</mml:mo> <mml:mi>N</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> spontaneous symmetry breaking
Bibliographic record
Abstract
We construct and study the relativistic Gross-Neveu-Yukawa field theory for the $\text{SO}(2N)$ real symmetric second-rank tensor order parameter coupled to ${N}_{f}$ flavors of $4N$-component Majorana fermions in $2+1$ dimensions. Such a tensor order parameter unifies all Lorentz-invariant mass-gap orders for $N$ two-component Dirac fermions in two dimensions except for the $\text{SO}(2N)$-singlet anomalous quantum Hall state. The value ${N}_{f}=1$ corresponds to the canonical Gross-Neveu model. Within the leading-order $\ensuremath{\epsilon}$-expansion around the upper critical dimension of $3+1$, the field theory exhibits a critical fixed point in its renormalization group flow which describes spontaneous symmetry breaking to $\text{SO}(N)\ifmmode\times\else\texttimes\fi{}\text{SO}(N)$ for the number of flavors of Majorana fermions higher than a critical value ${N}_{f,c2}\ensuremath{\approx}2N$. For ${N}_{f,c1}<{N}_{f}<{N}_{f,c2}$, with ${N}_{f,c1}\ensuremath{\approx}N$, the critical fixed point resides in the unstable region of the theory where the effective potential is unbounded from below, whereas for ${N}_{f}<{N}_{f,c1}$ there is no real critical fixed point and the flow runs away. In either case, for ${N}_{f}<{N}_{f,c2}$ the transition should become fluctuation-induced first order, and we discuss the dependence of its size on the parameters $N$ and ${N}_{f}$ in the theory. One-loop critical exponents for the universality class at ${N}_{f,c2}<{N}_{f}$ are computed and the flow diagram in various regimes is discussed.
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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 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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".