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Deformed Double Current Algebras, Matrix Extended $\mathcal W_{\infty}$ Algebras, Coproducts, and Intertwiners from the M2-M5 Intersection
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...
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Lenguaje: | eng |
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2023
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Acceso en línea: | http://cds.cern.ch/record/2875963 |
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author | Gaiotto, Davide Rapčák, Miroslav Zhou, Yehao |
author_facet | Gaiotto, Davide Rapčák, Miroslav Zhou, Yehao |
author_sort | Gaiotto, Davide |
collection | CERN |
description | 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. |
id | cern-2875963 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2023 |
record_format | invenio |
spelling | cern-28759632023-10-19T02:16:31Zhttp://cds.cern.ch/record/2875963engGaiotto, DavideRapčák, MiroslavZhou, YehaoDeformed Double Current Algebras, Matrix Extended $\mathcal W_{\infty}$ Algebras, Coproducts, and Intertwiners from the M2-M5 Intersectionmath.QAMathematical Physics and Mathematicsmath.MPMathematical Physics and Mathematicsmath-phMathematical Physics and Mathematicshep-thParticle Physics - TheoryWe 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.arXiv:2309.16929oai:cds.cern.ch:28759632023-09-28 |
spellingShingle | math.QA Mathematical Physics and Mathematics math.MP Mathematical Physics and Mathematics math-ph Mathematical Physics and Mathematics hep-th Particle Physics - Theory Gaiotto, Davide Rapčák, Miroslav Zhou, Yehao Deformed Double Current Algebras, Matrix Extended $\mathcal W_{\infty}$ Algebras, Coproducts, and Intertwiners from the M2-M5 Intersection |
title | Deformed Double Current Algebras, Matrix Extended $\mathcal W_{\infty}$ Algebras, Coproducts, and Intertwiners from the M2-M5 Intersection |
title_full | Deformed Double Current Algebras, Matrix Extended $\mathcal W_{\infty}$ Algebras, Coproducts, and Intertwiners from the M2-M5 Intersection |
title_fullStr | Deformed Double Current Algebras, Matrix Extended $\mathcal W_{\infty}$ Algebras, Coproducts, and Intertwiners from the M2-M5 Intersection |
title_full_unstemmed | Deformed Double Current Algebras, Matrix Extended $\mathcal W_{\infty}$ Algebras, Coproducts, and Intertwiners from the M2-M5 Intersection |
title_short | Deformed Double Current Algebras, Matrix Extended $\mathcal W_{\infty}$ Algebras, Coproducts, and Intertwiners from the M2-M5 Intersection |
title_sort | deformed double current algebras, matrix extended $\mathcal w_{\infty}$ algebras, coproducts, and intertwiners from the m2-m5 intersection |
topic | math.QA Mathematical Physics and Mathematics math.MP Mathematical Physics and Mathematics math-ph Mathematical Physics and Mathematics hep-th Particle Physics - Theory |
url | http://cds.cern.ch/record/2875963 |
work_keys_str_mv | AT gaiottodavide deformeddoublecurrentalgebrasmatrixextendedmathcalwinftyalgebrascoproductsandintertwinersfromthem2m5intersection AT rapcakmiroslav deformeddoublecurrentalgebrasmatrixextendedmathcalwinftyalgebrascoproductsandintertwinersfromthem2m5intersection AT zhouyehao deformeddoublecurrentalgebrasmatrixextendedmathcalwinftyalgebrascoproductsandintertwinersfromthem2m5intersection |