论文标题
$ {\ cal n} = 2 $ supersymmetric $ w_ {1+ \ infty} $ symmetry在二维SYK模型中
The ${\cal N}=2$ Supersymmetric $w_{1+\infty}$ Symmetry in the Two-Dimensional SYK Models
论文作者
论文摘要
我们确定了二维$ {\ cal n} =（2,2）$ syk模型的级别$（q_ {syk} +1）$，具有变形参数$λ$在Bergshoeff，de wit and de wit and vasiliev（1991年）中的$λ$ $λ= \ frac {1} {2（q_ {syk} +1）} $通过使用矩阵概括。在消失的$λ$（或$ q_ {syk} $的无穷大限制）中，$ {\ cal n} = 2 $ supersymmetric linear $ w _ {\ infty}^{n，n} [λ= 0]通过意识到上述SYK模型中的$ n $ - 手掌多重和$ n $ -FERMI多重组的sibalgebra扮演着相同数量的$β\，γ$和$ b \，$ b \，c $ ghost Systems在线性$ w _ {\ infty}^{\ infty}^n，n，n，n}^{n，n} [n，n} [n} [n} [n} [n} [n} $ alge = 0] $ alge $ alge。对于非零$λ$，我们确定完整的$ {\ cal n} = 2 $ supersymmetric linear $ w _ {\ infty}^{n，n，n，n} [λ] $ algebra，其中结构常数由两种不同的通用超微观函数的线性组合给出，具有$λ$的$λ$依赖性。重量 - $ 1，\ frac {1} {2} $电流出现在该代数的右侧，其结构常数具有$λ$ ractor。我们还通过计算消失的结构常数来描述$λ= \ frac {1} {4} $（或$ q_ {syk} = 1 $）情况。
We identify the rank $(q_{syk}+1)$ of the interaction of the two-dimensional ${\cal N}=(2,2)$ SYK model with the deformation parameter $λ$ in the Bergshoeff, de Wit and Vasiliev(in 1991)'s linear $W_{\infty}[λ]$ algebra via $λ=\frac{1}{2(q_{syk}+1)}$ by using a matrix generalization. At the vanishing $λ$ (or the infinity limit of $q_{syk}$), the ${\cal N}=2$ supersymmetric linear $W_{\infty}^{N,N}[λ=0]$ algebra contains the matrix version of known ${\cal N}=2$ $W_{\infty}$ 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 $β\, γ$ and $b\, c$ ghost systems in the linear $W_{\infty}^{N,N}[λ=0]$ algebra. For the nonzero $λ$, we determine the complete ${\cal N}=2$ 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 $q_{syk}=1$) case in the truncated subalgebras by calculating the vanishing structure constants.
