论文标题
有限晶格理论中的大$ n $相过渡
A Large-$N$ Phase Transition in a Finite Lattice Gauge Theory
论文作者
论文摘要
我们考虑非亚伯利亚$有限$组的规格理论，并讨论排列组$ s_n $的1+1维晶格量表理论。有限$ n $的分区功能可以使用$ s_n $ conjugacy类的属性以紧凑的形式明确编写。具有新的't hooft耦合，$λ= g^2 \ log n $的天然大$ n $限制。我们在无限$ n $上确定了一个类似于wadia的水平的阶段过渡，$λ= 2 $。这是一阶。可以从Wilson循环期望值计算出弦张力的类似物，并且它从零跳到有限值。我们将其视为一种大型$ n $（DE-）禁闭过渡。简要讨论了我们考虑考虑此类理论的全息动机。
We consider gauge theories of non-Abelian $finite$ groups, and discuss the 1+1 dimensional lattice gauge theory of the permutation group $S_N$ as an illustrative example. The partition function at finite $N$ can be written explicitly in a compact form using properties of $S_N$ conjugacy classes. A natural large-$N$ limit exists with a new 't Hooft coupling, $λ=g^2 \log N$. We identify a Gross-Witten-Wadia-like phase transition at infinite $N$, at $λ=2$. It is first order. An analogue of the string tension can be computed from the Wilson loop expectation value, and it jumps from zero to a finite value. We view this as a type of large-$N$ (de-)confinement transition. Our holographic motivations for considering such theories are briefly discussed.
