Genus-2 holographic correlator on AdS5 × S5 from localization
Bibliographic record
Abstract
Abstract We consider the four-point function of the stress tensor multiplet superprimary in $$ \mathcal{N} $$ N = 4 super-Yang-Mills (SYM) with gauge group SU(N ) in the large N and large ’t Hooft coupling $$ \lambda \equiv {g}_{\mathrm{YM}}^2N $$ λ ≡ g YM 2 N limit, which is holographically dual to the genus expansion of IIB string theory on AdS5 × S 5. In [1] it was shown that the integral of this correlator is related to derivatives of the mass deformed $$ \mathcal{N} $$ N = 2 ∗ sphere free energy, which was computed using supersymmetric localization to leading order in 1/N 2 for finite λ. We generalize this computation to any order in 1/N 2 for finite λ using topological recursion, and use this any order constraint to fix the R 4 correction to the holographic correlator to any order in the genus expansion. We also use it to complete the derivation of the 1-loop supergravity correction, and show that analyticity in spin fails at zero spin in the large N expansion as predicted from the Lorentzian inversion formula. In the flat space limit, the R 4 term in the holographic correlator matches that of the IIB S-matrix in 10d, which is a precise check of AdS5/CFT4 for local operators at genus-one. Using the flat space limit and localization we then fix D 4 R 4 in the holographic correlator to any order in the genus expansion, which is nontrivial at genus-two, i.e. 1/N 6. This is the first result at two orders beyond the planar limit at strong coupling for a holographic correlator.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 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".