Abstract
We identify the rank (qsyk + 1) of the interaction of the two-dimensional \( \mathcal{N} \) = (2, 2) SYK model with the deformation parameter λ in the Bergshoeff, de Wit and Vasiliev (in 1991)’s linear W∞[λ] algebra via \( \lambda =\frac{1}{2\left({q}_{\mathrm{syk}}+1\right)} \) by using a matrix generalization. At the vanishing λ (or the infinity limit of qsyk), the \( \mathcal{N} \) = 2 supersymmetric linear \( {W}_{\infty}^{N,N} \)[λ = 0] algebra contains the matrix version of known \( \mathcal{N} \) = 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 \( {W}_{\infty}^{N,N} \)[λ = 0] algebra. For the nonzero λ, we determine the complete \( \mathcal{N} \) = 2 supersymmetric linear \( {W}_{\infty}^{N,N} \)[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, \( \frac{1}{2} \) currents occur in the right hand sides of this algebra and their structure constants have the λ factors. We also describe the λ = \( \frac{1}{4} \) (or qsyk = 1) case in the truncated subalgebras by calculating the vanishing structure constants.
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Ahn, C. The \( \mathcal{N} \) = 2 supersymmetric w1+∞ symmetry in the two-dimensional SYK models. J. High Energ. Phys. 2022, 115 (2022). https://doi.org/10.1007/JHEP05(2022)115
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DOI: https://doi.org/10.1007/JHEP05(2022)115