On the large <i>D</i> expansion of Hermitian multi-matrix models
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Bibliographic record
Abstract
We investigate the existence and properties of a double asymptotic expansion in 1/N2 and 1/D in U(N) × O(D) invariant Hermitian multi-matrix models, where the N × N matrices transform in the vector representation of O(D). The crucial point is to prove the existence of an upper bound η(h) on the maximum power D1+η(h) of D that can appear for the contribution at a given order N2−2h in the large N expansion. We conjecture that η(h) = h in a large class of models. In the case of traceless Hermitian matrices with the quartic tetrahedral interaction, we are able to prove that η(h) ≤ 2h; the sharper bound η(h) = h is proven for a complex bipartite version of the model, with no need to impose a tracelessness condition. We also prove that η(h) = h for the Hermitian model with the sextic wheel interaction, again with no need to impose a tracelessness condition.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.000 |
| 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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