Resurgence in Liouville theory
Bibliographic record
Abstract
A bstract Liouville conformal field theory is a prototypical example of an exactly solvable quantum field theory, in the sense that the correlation functions in an arbitrary background can be determined exactly using only the constraints of unitarity and crossing symmetry. For example, the three point correlation functions are given by the famous formula of Dorn-Otto-Zamolodchikov-Zamolodchikov (DOZZ). Unlike many other exactly solvable theories, Liouville theory has a continuously tunable parameter — essentially ℏ — which is related to the central charge of the theory. Here we investigate the nature of the perturbative expansion in powers of ℏ, which is the loop expansion around a semi-classical solution. We show that the perturbative coefficients grow factorially, as expected of a Feynman diagram expansion, and take the form of an asymptotic series. We identify the singularities in the Borel plane, and show that they are associated with complex instanton solutions of Liouville theory; they correspond precisely to the complex solutions described by Harlow, Maltz, and Witten. Both single- and multi-valued solutions of Liouville appear. We show that the perturbative loop expansions around these different saddle points mix in the way expected for a trans-series expansion. Thus Liouville theory provides a calculable example of a quantum field theory where perturbative and instanton contributions can be summed up and assembled into a finite answer.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".