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Loop equations for generalised eigenvalue models
by Edoardo Vescovi, Konstantin Zarembo
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Submission summary
| Authors (as registered SciPost users): | Konstantin Zarembo |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2402.13835v3 (pdf) |
| Date accepted: | 2024-06-18 |
| Date submitted: | 2024-06-13 19:13 |
| Submitted by: | Zarembo, Konstantin |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We derive the loop equation for the 1-matrix model with generic difference-type measure for eigenvalues and develop a recursive algebraic framework for solving it to an arbitrary order in the coupling constant in and beyond the planar approximation. The planar limit is solved exactly for a one-parametric family of models and in the general case at strong coupling. The Wilson loop in the N=2* super-Yang-Mills theory and the Hoppe model are used to illustrate our methods.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
highly relevant for our work. These results and ours, we believe, are complementary as we mostly discuss genus-0
expectation values. Those are treated as an input in 1303.5808, 1307.4957 to generate
the whole topological expansion (if we misinterpret these results we are open for further suggestions).
We added a paragraph in the introduction on the relation of our work to 1303.5808, 1307.4957, and also comment on it in the beginning
of the conclusions.
List of changes
- Added refs [13] and [14]
- Added the fourth paragraph on p. 2 and the second paragraph in sec. 7 discussing the relation between this work and our results
Published as SciPost Phys. 17, 017 (2024)
Reports on this Submission
Report
The authors have included references to the work on topological recursion and commented on the relation to them, as requested. I now recommend publication.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)