论文标题
双缩放Syk的散装希尔伯特空间
The bulk Hilbert space of double scaled SYK
论文作者
论文摘要
散装希尔伯特空间的出现是全息图中的一个神秘概念。在ARXIV：1811.02584中，通过求和和弦图以双缩放限制求解SYK模型。在这里，我们通过切片打开这些和弦图来明确构建双缩放Syk的散装希尔伯特空间。这个希尔伯特的空间类似于晶格场理论，其中晶格的长度是动力的，并由和弦数确定。在可计算的散装到边界地图下，固定和弦数映射的状态映射到具有相应大小的特定纠缠的2面状态。即使量子重力效应很重要，这种大量重建也是明确的。在双缩放的希尔伯特空间上作用是II型$ _1 $ observables的代数，其中包括哈密顿和物质运营商。在适当的量子Schwarzian极限中，我们还确定了JT引力代数，包括物理SL（2，R）对称发生器，并使用和弦图技术获得代数的明确表示。
The emergence of the bulk Hilbert space is a mysterious concept in holography. In arXiv:1811.02584, the SYK model was solved in the double scaling limit by summing chord diagrams. Here, we explicitly construct the bulk Hilbert space of double scaled SYK by slicing open these chord diagrams; this Hilbert space resembles that of a lattice field theory where the length of the lattice is dynamical and determined by the chord number. Under a calculable bulk-to-boundary map, states of fixed chord number map to particular entangled 2-sided states with a corresponding size. This bulk reconstruction is well-defined even when quantum gravity effects are important. Acting on the double scaled Hilbert space is a Type II$_1$ algebra of observables, which includes the Hamiltonian and matter operators. In the appropriate quantum Schwarzian limit, we also identify the JT gravitational algebra including the physical SL(2,R) symmetry generators, and obtain explicit representations of the algebra using chord diagram techniques.
