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Fermi-gas correlators of ADHM theory and triality symmetry
by Yasuyuki Hatsuda, Tadashi Okazaki
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Submission summary
Authors (as registered SciPost users): | Tadashi Okazaki |
Submission information | |
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Preprint Link: | scipost_202108_00070v1 (pdf) |
Date submitted: | Aug. 30, 2021, 2:43 p.m. |
Submitted by: | Okazaki, Tadashi |
Submitted to: | SciPost Physics |
Ontological classification | |
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Academic field: | Physics |
Specialties: |
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Approach: | Theoretical |
Abstract
We analytically study the Fermi-gas formulation of sphere correlation functions of the Coulomb branch operators for 3d $\mathcal{N}=4$ ADHM theory with a gauge group $U(N)$, an adjoint hypermultiplet and $l$ hypermultiplets which can describe a stack of $N$ M2-branes at $A_{l-1}$ singularities. We find that the leading coefficients of the perturbative grand canonical correlation functions are invariant under a hidden triality symmetry conjectured from the twisted M-theory. The triality symmetry also helps us to fix the next-to-leading corrections analytically.
Current status:
Reports on this Submission
Report #3 by Anonymous (Referee 3) on 2021-9-29 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202108_00070v1, delivered 2021-09-29, doi: 10.21468/SciPost.Report.3591
Report
I believe that the results and the techniques in this manuscript will be interesting to other researchers working on localization in supersymmetric gauge theories, matrix models, AdS/CFT correspondence and related topics. The paper is generally well written. I would like to recommend it for publication.
Requested changes
I have the following minor suggestions which I think can improve the readability of the paper, particularly for non-specialists:
1) From the expressions (2.8) it seems that the Wigner transform of the Hamiltonian $H_W$ is generically complex valued (in particular its classical part) . Later $(2\pi\mu/\epsilon_1-H_W)$ appears as the argument of the functions like Heaviside step function and Dirac delta function, which are ordinarily defined for a real argument only. I think it would be better if the authors add a clarification about interpretation of such expressions.
2) In the beginning of Section 3 the authors use subscript $n_*$. I suggest that the authors add a comment on what is its meaning, what is the range of the sum in (3.1), and why only $n_*=0$ appears in (3.2).
3) In the formulas like (3.52) (similarly in (3.61)) the authors may consider indicating dependence of $\langle \mathcal{O}\rangle$ on $N$ inside the sum more explicitly , otherwise the formula looks a little confusing.
4) I find that the manuscript in some places (for example around pages 12, 18-21) is quite heavy on technical details which are rather elementary (like calculation of integrals). I think moving them to Appendix might make the reading of the paper more enjoyable. But I leave it up to the authors.
Report #2 by Jihwan Oh (Referee 2) on 2021-9-28 (Invited Report)
- Cite as: Jihwan Oh, Report on arXiv:scipost_202108_00070v1, delivered 2021-09-28, doi: 10.21468/SciPost.Report.3584
Report
Overall, this paper has top quality. Therefore, without further editing, I recommend to publish it.
Report #1 by Anonymous (Referee 1) on 2021-9-26 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202108_00070v1, delivered 2021-09-26, doi: 10.21468/SciPost.Report.3570
Report
The analyses of the correlation function are completely original results of the paper. Also, although the large N expansion of the $S^3$ partition function was already obtained in a previous research in a dual description by an ABJM-like theory, the re-interpretation in the omega-deformed M-theory is new. For these reasons I recommend this paper to be published.