2025/12/18 by Abedin, Raschid, Niu, Wenjun
#17B37 #17B69 #81R50 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2512.16996
In this paper, we construct the dual Y^*_ℏ(\mathfrak d) and double DY_ℏ (\mathfrak d) of the Yangian Y_ℏ (\mathfrak d) associated with a cotangent Lie algebra \mathfrak d=T^*\mathfrak g. We define a coherent factorization algebra version of the dual Yangian Y_ℏ^*(\mathfrak d)co-op with opposite coproduct. Furthermore, we define a quantum vertex algebra structure on the quantum vacuum module Vℏ,k(\mathfrak d) of central extensions \widehatDYℏ,ℓ (\mathfrak d) of this double Yangian and show that its conformal blocks satisfy quantum KZ equations. We discuss examples of \mathfrak d that arise from 3d N=4 gauge theories via the work of Costello-Gaiotto. These examples include Takiff Lie algebras T^*\mathfrak g, whose affine VOA is a large subalgebra of the chiral differential operator algebra of G, as well as the smallest type-A Lie superalgebra \mathfrakgl (1|1).