Deformed Double Current Algebras, Matrix Extended \mathcal W_∞ Algebras, Coproducts, and Intertwiners from the M2-M5 Intersection

2023/09/29 by Gaiotto, Davide, Rapčák, Miroslav, Zhou, Yehao
#16T10 (Primary) 81T30 #81T32 #81T40 #81T70 (Secondary) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2309.16929

Abstract

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 \mathfrakgl_K and \mathfrakgl_K-extended W_∞-algebra respectively. We give a new presentation of the deformed double current algebra of \mathfrakgl_K, and we give a rigorous mathematical construction of the \mathfrakgl_K-extended W_∞-algebra. A new presentation of the affine Yangian of \mathfrakgl_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.

Related

• Miura operators, degenerate fields and the M2-M5 intersection
• R-matrices from Feynman Diagrams in 5d Chern-Simons Theory and Twisted M-theory
• The \cal N=2,4 Supersymmetric Linear W_∞[λ] Algebras for Generic λ Parameter
• Miura operators as R-matrices from M-brane intersections
• Extensions of deformed W-algebras via qq-characters