Spread complexity for the planar limit of holography
Bibliographic record
Abstract
Complexity is a fundamental characteristic of states within a quantum system. Its use is however mostly limited to bosonic systems, inhibiting its present applicability to supersymmetric theories. This is also relevant to its application to the AdS/CFT correspondence. To address this limitation, we extend the framework of spread complexity beyond bosonic systems to include fermionic and supercoherent states. This offers a gateway to compute spread complexity analytically for any semiclassical system governed by a Hamiltonian associated with a Lie (super)algebra. This requires extending the Krylov chain to a Krylov path in a higher-dimensional lattice. A detailed analysis of supercoherent states within the super Heisenberg-Weyl and OSp$(2|1)$ algebras elucidates distinct contributions from bosonic and fermionic degrees of freedom to the complexity. This generalisation allows us to access the semiclassical regime of the planar limit of the holographic correspondence. We then compute the spread complexity of large charge superstring states on the gravity side, which are equivalent to the dual gauge states. The resulting complexity leads to Krylov paths capturing the geometry in which the string propagates.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".