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Matrix models for extremal and integrated correlators of higher rank
by Alba Grassi, Cristoforo Iossa
Submission summary
| Authors (as registered SciPost users): | Cristoforo Iossa |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2408.07391v1 (pdf) |
| Date submitted: | Oct. 27, 2025, 4:03 p.m. |
| Submitted by: | Cristoforo Iossa |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study extremal and integrated correlators of half-BPS operators in four-dimensional $\mathcal{N}=2$ SQCD and $\mathcal{N}=4$ SYM with $SU(3)$ gauge group. We focus on the large R-charge sector where the number of operators insertions becomes very large. In this regime, we demonstrate that the correlators are described by a combination of Wishart and Jacobi matrix models, coupled in a non-trivial way. The size of the matrices in each model corresponds to the maximal number of insertions for each of the two single trace generators. This dual matrix model representation allows us to extract the behavior of the correlators at weak and strong coupling in a 't Hooft-like double scaling limit, including nonperturbative corrections. Although this work focuses on $SU(3)$, we expect that our techniques can be extended to $SU(N)$ for $N>3$ as well.
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This paper investigates the large-charge behaviour of extremal correlators in SU(3) SQCD and integrated correlators in SU(3) N=4 SYM. Unlike the rank-1 case, starting from SU(3) there exist many distinct operators with the same charges (equivalently, dimensions). Consequently, there are multiple different ways to take the large-charge limit, leading to a much richer dynamical structure than in rank-1 theories. The physical observables studied here are of important interest, and related topics have been an active research area.
These extremal correlators and integrated correlators can be computed exactly via supersymmetric localization. The authors analyse the resulting matrix models and show that, in a large-charge ’t Hooft limit, the results can be described in terms of certain dual effective matrix models. These dual matrix models allow one to efficiently extract various large-charge asymptotics and to explore the associated physical properties.
The paper is clearly written, and the results are new, interesting; and in some cases it helps clarify previous statements in the literature. I believe the paper is suitable for publication in SciPost.
Before publication, the authors may wish to consider the following points:
- Some proofreading may be helpful.
For example, in (2.61), I believe $Z_{\rm inst}$ should depend on $\tau_A$, due to the insertion of higher-dimensional operators. This of course does not affect any of the results, since instanton contribution was not considered in the paper.
In (5.49), it seems $dx$ is missing. In the paragraph after (5.53), the poles at $s=0, 1$ should be $s=0, -1$, and similarly $s= {2n+1 \over 2}$ should be $s=- {2n+1 \over 2}$.
Before (6.80), "... $|\kappa|<k^* = 1/8$ From (6.73) ... " should be "... $|\kappa|<k^* = 1/8$. From (6.73) ... ", namely a 'period' is missing.
A typo before (C.11), where "dacay" should be "decay", and $dz$ is missing in (C.11).
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Is the "$n$" that appears in the subscript of $\mathcal{O}_{n+3 \ell}^{(m-2\ell)}$ in (3.7) a typo? Should it be removed?
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The notations ${\rm disc}(1/z)$ in (C.11) and ${\rm disc}(\kappa)$ in (C.12) are slightly confusing. As far as I can tell, they are not describing the discontinuities of $1/z$ and $\kappa$.
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Finally, It’s worth mentioning that some of the large-charge properties of certain integrated correlators in N=4 SYM with SU(N) gauge group have been considered in the literature. In particular, the operators constructed in (2.51) (2.52) have also appeared and studied in 2407.02250 (namely ref. [45] of the paper).
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Publish (easily meets expectations and criteria for this Journal; among top 50%)
Strengths
- detailed computations
- cases that have not appeared in literature -new computational methods
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Requested changes
i suggest the authors to run a spell check since i found few typos
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)