The N = 2 supersymmetric w1+∞ symmetry in the two-dimensional SYK models

A bstract We identify the rank (q syk + 1) of the interaction of the two-dimensional N N = (2, 2) SYK model with the deformation parameter λ in the Bergshoeff, de Wit and Vasiliev (in 1991) ’s linear W ∞ λ algebra via =12 ({qₒₘ₊+1) } λ = 1 2 q syk + 1 by using a matrix generalization. At the vanishing λ (or the infinity limit of q syk), the N N = 2 supersymmetric linear W_^N, N W ∞ N, N λ = 0 algebra contains the matrix version of known N N = 2 W ∞ algebra, as a subalgebra, by realizing that the N -chiral multiplets and the N -Fermi multiplets in the above SYK models play the role of the same number of βγ and bc ghost systems in the linear W_^N, N W ∞ N, N λ = 0 algebra. For the nonzero λ, we determine the complete N N = 2 supersymmetric linear W_^N, N W ∞ N, N λ algebra where the structure constants are given by the linear combinations of two different generalized hypergeometric functions having the λ dependence. The weight-1, 12 1 2 currents occur in the right hand sides of this algebra and their structure constants have the λ factors. We also describe the λ = 14 1 4 (or q syk = 1) case in the truncated subalgebras by calculating the vanishing structure constants.