发表机构
Institute for Information Transmission Problems RAS; Moscow Institute of Physics and Technology; Phystech School of Applied Mathematics and Computer Science, Moscow Institute for Physics and Technology; LPTMS, CNRS – Université Paris Saclay（俄罗斯科学院信息传输问题研究所; 莫斯科物理技术学院; 莫斯科物理技术学院应用数学与计算机科学普列谢耶夫学院; CNRS-巴黎萨克雷大学理论物理实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文揭示了KPZ类随机增长模型、DSSYK与二维膨胀引力间的三重对偶，将TASEP等同强耦合量子引力，推导ASEP预解式，并建立与Tutte多项式及堆模型的联系。
AI 中文摘要
我们讨论了KPZ普适类中的随机增长模型、DSSYK模型以及低维膨胀引力之间的三重对偶性。TASEP模型是我们的主要关注对象，它被等同于二维量子引力的强耦合极限。DSSYK的哈密顿量与ASEP的转移矩阵在相差一个加性常数的情况下一致，我们推导了有限区间上ASEP相应转移矩阵的预解式的精确表达式。我们还提到了累积量与弦图对偶的交叉图的Tutte多项式$T(1,q)$之间的关系，这暗示了所考虑的模型与耦合引力的$Q=0$ Potts模型之间的联系。我们进一步利用所有这些模型在二维流形上的离散和连续随机游走的不同版本中的实现，这些随机游走参数化了各自理论的希尔伯特空间。将TASEP表示为堆的增长模型为强耦合引力提供了新的见解，暗示其可被解释为一种涌现现象。我们还发展了ASEP与q-TASEP模型以及堆模型之间的新对偶性，为增长提供了有用的解释。
英文摘要
We discuss the triality between stochastic growth models in the KPZ universality class, the DSSYK model, and low dimensional dilaton gravity. The TASEP model, which will be our primary focus, is identified with the strong-coupling limit of two-dimensional quantum gravity. The Hamiltonian of DSSYK and the transfer matrix of ASEP coincide up to an additive constant, and we derive the exact expression for the resolvent of the corresponding transfer matrix in ASEP on a finite interval. We also mention the relation of cumulants with the Tutte polynomial $T(1,q)$ of the crossing graph dual to the chord diagram, which implies the relationship of the models considered with the $Q=0$ Potts model coupled with gravity. We further exploit the realization of all these models in terms of different versions of discrete and continuous random walks on two-dimensional manifolds, which parameterize the Hilbert spaces of the respective theories. The representation of TASEP as the growth model of heaps provides new insight into strong-coupling gravity, suggesting its interpretation as an emerging phenomenon. The new dualities between ASEP and q-TASEP models and heap models providing a useful growth interpretation have been developed.
Comments80 pages, 5 figures
