R-matrices and Miura operators in 5d Chern-Simons theory
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 tran...
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2025-01-01
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| Series: | SciPost Physics Core |
| Online Access: | https://scipost.org/SciPostPhysCore.8.1.003 |
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| author | Nafiz Ishtiaque, Saebyeok Jeong, Yehao Zhou |
| author_facet | Nafiz Ishtiaque, Saebyeok Jeong, Yehao Zhou |
| author_sort | Nafiz Ishtiaque, Saebyeok Jeong, Yehao Zhou |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-931f63e8016d42df84c1c7b98496f30a |
| institution | Kabale University |
| issn | 2666-9366 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics Core |
| spelling | doaj-art-931f63e8016d42df84c1c7b98496f30a2025-01-13T11:16:21ZengSciPostSciPost Physics Core2666-93662025-01-018100310.21468/SciPostPhysCore.8.1.003R-matrices and Miura operators in 5d Chern-Simons theoryNafiz Ishtiaque, Saebyeok Jeong, Yehao ZhouWe 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.https://scipost.org/SciPostPhysCore.8.1.003 |
| spellingShingle | Nafiz Ishtiaque, Saebyeok Jeong, Yehao Zhou R-matrices and Miura operators in 5d Chern-Simons theory SciPost Physics Core |
| title | R-matrices and Miura operators in 5d Chern-Simons theory |
| title_full | R-matrices and Miura operators in 5d Chern-Simons theory |
| title_fullStr | R-matrices and Miura operators in 5d Chern-Simons theory |
| title_full_unstemmed | R-matrices and Miura operators in 5d Chern-Simons theory |
| title_short | R-matrices and Miura operators in 5d Chern-Simons theory |
| title_sort | r matrices and miura operators in 5d chern simons theory |
| url | https://scipost.org/SciPostPhysCore.8.1.003 |
| work_keys_str_mv | AT nafizishtiaquesaebyeokjeongyehaozhou rmatricesandmiuraoperatorsin5dchernsimonstheory |