Deformed Double Current Algebras, Matrix Extended $\mathcal W_{\infty}$ Algebras, Coproducts, and Intertwiners from the M2-M5 Intersection
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913284227072000 |
|---|---|
| author | Gaiotto, Davide Rapčák, Miroslav Zhou, Yehao |
| author_facet | Gaiotto, Davide Rapčák, Miroslav Zhou, Yehao |
| contents | We study the algebraic structures which govern the deformation of supersymmetric intersections of M2 and M5 branes. The universal algebras on M2 and M5 branes are deformed double current algebra of $\mathfrak{gl}_K$ and $\mathfrak{gl}_K$-extended $\mathcal{W}_{\infty}$-algebra respectively. We give a new presentation of the deformed double current algebra of $\mathfrak{gl}_K$, and we give a rigorous mathematical construction of the $\mathfrak{gl}_K$-extended $\mathcal{W}_{\infty}$-algebra. A new presentation of the affine Yangian of $\mathfrak{gl}_K$ is also obtained. We construct various coproducts of these algebras, which are expected to encode the fusions of defects in twisted M-theory. The matrix extended Miura operators are identified as intertwiners in certain bimodules of these algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_16929 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Deformed Double Current Algebras, Matrix Extended $\mathcal W_{\infty}$ Algebras, Coproducts, and Intertwiners from the M2-M5 Intersection Gaiotto, Davide Rapčák, Miroslav Zhou, Yehao High Energy Physics - Theory Mathematical Physics Quantum Algebra 16T10 (Primary) 81T30, 81T32, 81T40, 81T70 (Secondary) We study the algebraic structures which govern the deformation of supersymmetric intersections of M2 and M5 branes. The universal algebras on M2 and M5 branes are deformed double current algebra of $\mathfrak{gl}_K$ and $\mathfrak{gl}_K$-extended $\mathcal{W}_{\infty}$-algebra respectively. We give a new presentation of the deformed double current algebra of $\mathfrak{gl}_K$, and we give a rigorous mathematical construction of the $\mathfrak{gl}_K$-extended $\mathcal{W}_{\infty}$-algebra. A new presentation of the affine Yangian of $\mathfrak{gl}_K$ is also obtained. We construct various coproducts of these algebras, which are expected to encode the fusions of defects in twisted M-theory. The matrix extended Miura operators are identified as intertwiners in certain bimodules of these algebras. |
| title | Deformed Double Current Algebras, Matrix Extended $\mathcal W_{\infty}$ Algebras, Coproducts, and Intertwiners from the M2-M5 Intersection |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Algebra 16T10 (Primary) 81T30, 81T32, 81T40, 81T70 (Secondary) |
| url | https://arxiv.org/abs/2309.16929 |