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R-matrices and Miura operators in 5d Chern-Simons theory
by Nafiz Ishtiaque, Saebyeok Jeong, Yehao Zhou
Submission summary
| Authors (as registered SciPost users): | Saebyeok Jeong |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2408.15712v2 (pdf) |
| Date submitted: | 2024-11-19 09:54 |
| Submitted by: | Jeong, Saebyeok |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We derive Miura operators for $W$- and $Y$-algebras from first principles as the expectation value of the intersection between a topological line defect and a holomorphic surface defect in 5-dimensional non-commutative $\mathfrak{gl}(1)$ Chern-Simons theory. The expectation value, viewed as the transition amplitude for states in the defect theories forming representations of the affine Yangian of $\mathfrak{gl}(1)$, satisfies the Yang-Baxter equation and is thus interpreted as an R-matrix. To achieve this, we identify the representations associated with the line and surface defects by calculating the operator product expansions (OPEs) of local operators on the defects, as conditions that anomalous Feynman diagrams cancel each other. We then evaluate the expectation value of the defect intersection using Feynman diagrams. When the line and surface defects are specified, we demonstrate that the expectation value precisely matches the Miura operators and their products.
Author comments upon resubmission
List of changes
Based on feedback from two reports, we have made the following revisions in the new version:
1. We have added Figure 1 to assist readers in understanding the geometric setup of the M2-M5 intersection.
2. Footnote 2 has been added to provide a remark on Koszul duality.
3. Footnote 3 includes a remark on the completed tensor product.
4. We have cited the work available at https://inspirehep.net/literature/2779492.
5. Footnote 4 has been added to clarify the origin of the constant B-field.
6. An explanation of the preserved supercharge has been included around equation (2.2).
7. The description of the topological descent procedure at the beginning of Section 2.2 has been improved, with additional citations.
8. In Footnote 7, we have detailed the errors in [41] that were corrected in our manuscript.
9. The origin of coproduct from defect fusion at the beginning of Section 4 has been clarified.
10. The opposite coproduct is now defined on page 27.
11. We have clarified that the perturbative computations for the OPEs on the surface defect and surface defect fusion were performed only up to the spin-2 generators.
12. All typos and spelling errors pointed out in the reports have been corrected.