论文标题
量子组，非交通$ ads_2 $以及双尺度模型中的和弦
Quantum groups, non-commutative $AdS_2$, and chords in the double-scaled SYK model
论文作者
论文摘要
我们研究SYK（DS-SYK）模型的双尺度极限，并阐明了基础量子组对称性。 DS-SYK模型的特征是参数$ Q $，在$ Q \ rightarrow 1 $和低能的限制中，它归功于熟悉的Schwarzian理论。我们将和弦和转移矩阵图片与Euclidean Poincar {é}磁盘上的“边界粒子”的运动相关联，它是单面Schwarzian模型的基础。 \ Mathfrak {s} \ Mathfrak {U}（1,1）$，我们认为完整的DS-Syk模型的对称性是后者的一定$ q $ - 元素，即$ \ \ Mathcal {U}通过获取DS-Syk的有效哈密顿量作为（减少）粒子在$ ads_2 $中移动的粒子，它具有此$ \ Mathcal {u} _ {\ sqrt q}（\ sqrt q}（\ mathfrak）通过获得$ Q $均匀空间的非共同几何形状，通过获得DS-Syk的有效哈密顿量作为（减少）粒子上的粒子的非交换变形，$ ads_3 $的家庭可能有可能独特的$ q $ ds $ ads_2 $的家庭。
We study the double-scaling limit of SYK (DS-SYK) model and elucidate the underlying quantum group symmetry. The DS-SYK model is characterized by a parameter $q$, and in the $q\rightarrow 1$ and low-energy limit it goes over to the familiar Schwarzian theory. We relate the chord and transfer-matrix picture to the motion of a ``boundary particle" on the Euclidean Poincar{é} disk, which underlies the single-sided Schwarzian model. $AdS_2$ carries an action of $\mathfrak{s}\mathfrak{l}(2,{\mathbb R}) \simeq \mathfrak{s}\mathfrak{u}(1,1)$, and we argue that the symmetry of the full DS-SYK model is a certain $q$-deformation of the latter, namely $\mathcal{U}_{\sqrt q}(\mathfrak{s}\mathfrak{u}(1,1))$. We do this by obtaining the effective Hamiltonian of the DS-SYK as a (reduction of) particle moving on a lattice deformation of $AdS_2$, which has this $\mathcal{U}_{\sqrt q}(\mathfrak{s}\mathfrak{u}(1,1))$ algebra as its symmetry. We also exhibit the connection to non-commutative geometry of $q$-homogeneous spaces, by obtaining the effective Hamiltonian of the DS-SYK as a (reduction of) particle moving on a non-commutative deformation of $AdS_3$. There are families of possibly distinct $q$-deformed $AdS_2$ spaces, and we point out which are relevant for the DS-SYK model.
