Deformed Double Current Algebras, Matrix Extended $\mathcal W_{\infty}$ Algebras, Coproducts, and Intertwiners from the M2-M5 Intersection

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Hauptverfasser: Gaiotto, Davide, Rapčák, Miroslav, Zhou, Yehao
Format: Preprint
Veröffentlicht: 2023
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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.
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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