标题： 双尺度SYK模型的动力学作用与q-表示论 显示英文标题

标题： Dynamical actions and q-representation theory for double-scaled SYK

摘要： 我们证明了通过考虑量子群SU$_q(1,1)$上受约束粒子的量子力学，可以重现DSSYK振幅。我们构建了其左正则表示和右正则表示，并展示了表示矩阵能够再现DSSYK的双侧波函数和相关函数。接着，我们为SU$_q(1,1)$上的粒子构造了一个动力学作用量和路径积分，其量子化可以重现上述表示理论。通过对边界条件加以限制或约束系统，我们找到了Schwarzian和Liouville边界路径积分描述的$q$类比。这为确定DSSYK的引力整体描述奠定了技术基础。我们发现所讨论的理论是一种正弦标量引力，有趣的是，它能够描述AdS和dS量子引力。 显示英文摘要

摘要： We show that DSSYK amplitudes are reproduced by considering the quantum mechanics of a constrained particle on the quantum group SU$_q(1,1)$. We construct its left-and right-regular representations, and show that the representation matrices reproduce two-sided wavefunctions and correlation functions of DSSYK. We then construct a dynamical action and path integral for a particle on SU$_q(1,1)$, whose quantization reproduces the aforementioned representation theory. By imposing boundary conditions or constraining the system we find the $q$-analog of the Schwarzian and Liouville boundary path integral descriptions. This lays the technical groundwork for identifying the gravitational bulk description of DSSYK. We find evidence the theory in question is a sine dilaton gravity, which interestingly is capable of describing both AdS and dS quantum gravity.