论文标题
集群变换，四面体方程和三维理论
Cluster transformations, the tetrahedron equation and three-dimensional gauge theories
论文作者
论文摘要
我们定义了三个Quivers家族，其中对称群体的辫子关系是通过突变和自动形态实现的。八个编织的序列以$ s_4 $的最长元素的简化单词移动，产生了三个微不足道的集群变换，具有8、32和32突变。对于这些集群变换中的每一个，代表单一编织的量子机械系统中的单位算子求解四面体方程。这样获得的溶液是由非恰当量子差异算法构造的，可以通过三维$ \ nathcal {n} = 2 $ supersympersmmetric仪表理论的分区函数来识别。
We define three families of quivers in which the braid relations of the symmetric group $S_n$ are realized by mutations and automorphisms. A sequence of eight braid moves on a reduced word for the longest element of $S_4$ yields three trivial cluster transformations with 8, 32 and 32 mutations. For each of these cluster transformations, a unitary operator representing a single braid move in a quantum mechanical system solves the tetrahedron equation. The solutions thus obtained are constructed from the noncompact quantum dilogarithm and can be identified with the partition functions of three-dimensional $\mathcal{N} = 2$ supersymmetric gauge theories on a squashed three-sphere.
