CFT4 as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mrow><mml:mi mathvariant="italic">SO</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>4</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>-invariant TFT2
Bibliographic record
Abstract
We show that correlators of local operators in four-dimensional free scalar field theory can be expressed in terms of amplitudes in a two-dimensional topological field theory (TFT2). We describe the state space of the TFT2, which has SO(4,2) as a global symmetry, and includes both positive and negative energy representations. Invariant amplitudes in the TFT2 correspond to surfaces interpolating from multiple circles to the vacuum. They are constructed from SO(4,2) invariant linear maps from the tensor product of the state spaces to complex numbers. When appropriate states labeled by 4D-spacetime coordinates are inserted at the circles, the TFT2 amplitudes become correlators of the four-dimensional CFT4. The TFT2 structure includes an associative algebra, related to crossing in the 4D-CFT, with a non-degenerate pairing related to the CFT inner product in the CFT4. In the free-field case, the TFT2/CFT4 correspondence can largely be understood as realization of free quantum field theory as a categorified form of classical invariant theory for appropriate SO(4,2) representations. We discuss the prospects of going beyond free fields in this framework.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.005 | 0.005 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.805 | 0.540 |
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".