Random Field Ising Model and Parisi-Sourlas supersymmetry. Part I. Supersymmetric CFT
Bibliographic record
Abstract
Abstract Quenched disorder is very important but notoriously hard. In 1979, Parisi and Sourlas proposed an interesting and powerful conjecture about the infrared fixed points with random field type of disorder: such fixed points should possess an unusual supersymmetry, by which they reduce in two less spatial dimensions to usual non-supersymmetric non- disordered fixed points. This conjecture however is known to fail in some simple cases, but there is no consensus on why this happens. In this paper we give new non-perturbative arguments for dimensional reduction. We recast the problem in the language of Conformal Field Theory (CFT). We then exhibit a map of operators and correlation functions from Parisi-Sourlas supersymmetric CFT in d dimensions to a (d − 2)-dimensional ordinary CFT. The reduced theory is local, i.e. it has a local conserved stress tensor operator. As required by reduction, we show a perfect match between superconformal blocks and the usual conformal blocks in two dimensions lower. This also leads to a new relation between conformal blocks across dimensions. This paper concerns the second half of the Parisi-Sourlas conjecture, while the first half (existence of a supersymmetric fixed point) will be examined in a companion work.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".