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.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.013 | 0.010 |
| Meta-epidemiology (narrow) | 0.009 | 0.015 |
| Meta-epidemiology (broad) | 0.005 | 0.018 |
| Bibliometrics | 0.004 | 0.011 |
| Science and technology studies | 0.009 | 0.012 |
| Scholarly communication | 0.009 | 0.008 |
| Open science | 0.016 | 0.013 |
| Research integrity | 0.010 | 0.015 |
| Insufficient payload (model declined to judge) | 0.070 | 0.019 |
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; both teacher heads agree on what is shown here.
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".