Conformal four-point correlators of the 3D Ising transition via the quantum fuzzy sphere
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Bibliographic record
Abstract
In conformal field theory (CFT), the four-point correlator is a fundamental object that encodes CFT properties, constrains CFT structures, and connects to the gravitational scattering amplitude in holography theory. However, the four-point correlator of CFTs in dimensions higher than 2D remains largely unexplored due to the lack of non-perturbative tools. In this paper, we introduce a new approach for directly computing four-point correlators of 3D CFTs. Our method employs the recently proposed fuzzy (non-commutative) sphere regularization, and we apply it to the paradigmatic 3D Ising CFT. Specifically, we have computed three different four-point correlators: $\langle σσσσ\rangle$, $\langle σσεε\rangle$, and $\langle σσT_{μν} T_{ρη}\rangle$. Additionally, we verify the crossing symmetry of $\langle σσσσ\rangle$, which is a notable property arising from conformal symmetry. Remarkably, the computed four-point correlators exhibit continuous crossing ratios, showcasing the continuum nature of the fuzzy sphere regularization scheme. This characteristic renders them highly suitable for future theoretical applications, enabling further advancements and insights in 3D CFT.
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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 | 0.000 | 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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