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Proving superintegrability in $\beta$-deformed eigenvalue models
by Aditya Bawane, Pedram Karimi, Piotr Sułkowski
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Aditya Bawane |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2206.14763v1 (pdf) |
| Date accepted: | 2022-08-18 |
| Date submitted: | 2022-07-04 15:57 |
| Submitted by: | Bawane, Aditya |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In this note we provide proofs of various expressions for expectation values of symmetric polynomials in $\beta$-deformed eigenvalue models with quadratic, linear, and logarithmic potentials. The relations we derive are also referred to as superintegrability. Our work completes proofs of superintegrability statements conjectured earlier in literature.
Published as SciPost Phys. 13, 069 (2022)
Reports on this Submission
Report #2 by Anonymous (Referee 1) on 2022-8-16 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2206.14763v1, delivered 2022-08-16, doi: 10.21468/SciPost.Report.5545
Report
This paper deals with the superintegrability relations for beta deformed Hermitian matrix model. These relations has been conjectured previously and different numerical checks have been performed, however it was hard to prove those relations mainly due to the technical issues. This work presents the direct proof of those relations. I think that the paper is well-written and it deserves to be published.
Report #1 by Anonymous (Referee 2) on 2022-7-19 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2206.14763v1, delivered 2022-07-19, doi: 10.21468/SciPost.Report.5420
Report
I know this paper.
It describes the author's progress in understanding the "superintegrability" property of eigenvalue matrix models
(the fact that averages of distinguished quantities factorize
in especially nice way, somewhat unexpectedly) .
This is a fresh subject of significant importance,
both technical and conceptual,
probably not restricted to matrix models.
The paper confirms and proves some earlier conjectures.
I think that it deserves publication.