Nonperturbative tests of three-dimensional dualities
Nonperturbative tests of three-dimensional dualities
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三维二元性的非微扰检验
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Itamar Yaakov
中科院分区：
文献类型：
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作者：
A. Kapustin;Brian Willett;Itamar Yaakov
我们测试强耦合超共形场论在三维空间中的几个几何对偶计算其精确的配分函数的三个领域作为一个功能的Fayet-Iliopoulos和质量参数。计算进行了使用本地化的路径积分和矩阵模型先前导出的超共形$ \mathcal{N} = 2 $$规范理论。我们验证了由镜像对称性相关的量子理论的配分函数，只要质量参数和Fayet-Iliopoulos参数交换，如预测的那样。对超杨-米尔斯理论的镜像N = 8进行了类似的计算，证明了在单位Chern-Simons水平上，它的配分函数与ABJM理论的配分函数一致.这为两个理论在共形极限中的猜想等价性提供了一个非微扰检验。
We test several conjectural dualities between strongly coupled superconformal field theories in three dimensions by computing their exact partition functions on a three sphere as a function of Fayet-Iliopoulos and mass parameters. The calculation is carried out using localization of the path integral and the matrix model previously derived for superconformal $$ \mathcal{N} = 2 $$ gauge theories. We verify that the partition functions of quiver theories related by mirror symmetry agree provided the mass parameters and the Fayet-Iliopoulos parameters are exchanged, as predicted. We carry out a similar calculation for the mirror of $$ \mathcal{N} = 8 $$ super-Yang-Mills theory and show that its partition function agrees with that of the ABJM theory at unit Chern-Simons level. This provides a nonperturbative test of the conjectural equivalence of the two theories in the conformal limit.