将对偶性扩展到试验性深化了动力学的基础
Extending dualities to trialities deepens the foundations of dynamics
摘要：
对偶通常被认为是基础的，但它们可能与背景独立性发生冲突，因为需要一个隐藏的固定结构来定义对偶变换。这种冲突可以通过将二元性扩展为三元性来消除。这使固定结构成为动态的，同时将其与对偶变量统一起来。为了说明这一点，我们研究了具有立方作用的矩阵模型，并展示了如何通过施加不同的紧化来打破其自然的三重对称性，从而产生粒子力学、弦论和陈-西蒙斯理论。这些结果从紧化，分别为一，二，三个层面。这可以解释量子理论中位置算符和动量算符之间玻恩对偶的起源，以及弦论中的一些对偶。
英文摘要：
Dualities are often supposed to be foundational, but they may come into conflict with background independence, because a hidden fixed structures is needed to define the duality transformation. This conflict can be eliminated by extending a duality to a triality. This renders that fixed structure dynamical, while unifying it with the dual variables. To illustrate this, we study matrix models with a cubic action, and show how breaking its natural triality symmetry by imposing different compactifications yields particle mechanics, string theory and Chern-Simons theory. These result from compactifying, respectively, one, two and three dimensions. This may explain the origin of Born's duality between position and momenta operators in quantum theory, as well as some of the the dualities of string theory.
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