论文标题
$ \ MATHCAL {N} = 2 $ SUPERCON -CORMON -CORMONGAL TREMAIRE的平面限制
The planar limit of $\mathcal{N}=2$ superconformal quiver theories
论文作者
论文摘要
我们计算自由能的平面限制和四维$ {\ cal n} = 2 $ Super-Congrongulal Quiver Theories的$ 1/2 $ BPS Wilson Loop的期望值，并带有SU（$ n $）S的产品（$ n $）作为仪表集团和双向资源。超对称定位将问题降低为多矩阵模型，我们在零-instanton部门中重写是一种有效的动作，涉及由相关扩展的cartan矩阵确定的无限数量的双跟踪项。我们发现，与$ \ Mathcal {n} = 2 $ scfts的结果一样，可以用简单的量规组写入“树图上的总和”。对于$ \ wideHat {a_1} $ case，我们发现每棵树的贡献可以解释为在树上定义的广义ISING模型的分区函数；我们猜想这些在树上定义的模型的分区功能满足Lee-Yang特性，即它们的所有零位于单位圆上。
We compute the planar limit of both the free energy and the expectation value of the $1/2$ BPS Wilson loop for four dimensional ${\cal N}=2$ superconformal quiver theories, with a product of SU($N$)s as gauge group and bi-fundamental matter. Supersymmetric localization reduces the problem to a multi-matrix model, that we rewrite in the zero-instanton sector as an effective action involving an infinite number of double-trace terms, determined by the relevant extended Cartan matrix. We find that the results, as in the case of $\mathcal{N}=2$ SCFTs with a simple gauge group, can be written as sums over tree graphs. For the $\widehat{A_1}$ case, we find that the contribution of each tree can be interpreted as the partition function of a generalized Ising model defined on the tree; we conjecture that the partition functions of these models defined on trees satisfy the Lee-Yang property, i.e. all their zeros lie on the unit circle.
