R-matrices from Feynman Diagrams in 5d Chern-Simons Theory and Twisted M-theory
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917761495597056 |
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| author | Ashwinkumar, Meer |
| author_facet | Ashwinkumar, Meer |
| contents | In this work we study the analogues of R-matrices that arise in 5d non-commutative topological-holomorphic Chern-Simons theory, which is known to describe twisted M-theory. We first study the intersections of line and surface operators in 5d Chern-Simons theory, which correspond to M2- and M5-branes, respectively. A Feynman diagram computation of the correlation function of this configuration furnishes an expression reminiscent of an R-matrix derivable from 4d Chern-Simons theory. We explain how this object is related to a Miura operator that is known to realize (matrix-extended) $W_{\infty}$-algebras. For 5d Chern-Simons theory with nonabelian gauge group, we then perform a Feynman diagram computation of coproducts for deformed double current algebras and matrix-extended $W_{\infty}$-algebras from fusions of M2-branes, M5-branes, and M2-M5 intersections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15732 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | R-matrices from Feynman Diagrams in 5d Chern-Simons Theory and Twisted M-theory Ashwinkumar, Meer High Energy Physics - Theory Mathematical Physics Quantum Algebra In this work we study the analogues of R-matrices that arise in 5d non-commutative topological-holomorphic Chern-Simons theory, which is known to describe twisted M-theory. We first study the intersections of line and surface operators in 5d Chern-Simons theory, which correspond to M2- and M5-branes, respectively. A Feynman diagram computation of the correlation function of this configuration furnishes an expression reminiscent of an R-matrix derivable from 4d Chern-Simons theory. We explain how this object is related to a Miura operator that is known to realize (matrix-extended) $W_{\infty}$-algebras. For 5d Chern-Simons theory with nonabelian gauge group, we then perform a Feynman diagram computation of coproducts for deformed double current algebras and matrix-extended $W_{\infty}$-algebras from fusions of M2-branes, M5-branes, and M2-M5 intersections. |
| title | R-matrices from Feynman Diagrams in 5d Chern-Simons Theory and Twisted M-theory |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2408.15732 |