arXiv 1610.007402016-10hep-th

Higgs分支算符的一维理论

A one-dimensional theory for Higgs branch operators

Mykola Dedushenko, Silviu S. Pufu, Ran Yacoby

备注：: 108 pages; v2: typos corrected, some statements clarified

摘要：

我们利用超对称局部化方法计算了三维${\cal N} = 4$超共形场论中半BPS局部算子的关联函数，其拉格朗日描述由矢量多重态耦合到超多重态组成.我们主要研究的算子是希格斯分支算子的某些扭曲线性组合，它们可以沿着给定的线插入任何地方。这些算子是由超多重态标量构成的。它们构成了一个具有拓扑关联函数的一维非交换算子代数。全三维${\cal N}=4$理论中Higgs分支算符的2点和3点函数可以从一维拓扑代数中简单地推导出来。在将三维超共形场论从平坦空间共形映射到圆形三球面上之后，我们利用不属于${\cal N}=4$代数的任何三维${\cal N} = 2$子代数的超荷实现了超对称局域化.其结果是一个简单的模型，可以用来计算关联函数在一维拓扑代数上述。这个模型是一个耦合到矩阵模型的一维高斯理论，它可以被看作是拓扑规范量子力学的规范固定版本。我们的结果推广到非共形理论的$S^3$，包含真正的质量和Fayet-Iliopolous参数。我们还提供了与库仑分支相关的一维拓扑代数中的部分结果，在那里我们计算了从向量多重标量构建的局部算子的关联函数。

英文摘要：

We use supersymmetric localization to calculate correlation functions of half-BPS local operators in 3d ${\cal N} = 4$ superconformal field theories whose Lagrangian descriptions consist of vectormultiplets coupled to hypermultiplets. The operators we primarily study are certain twisted linear combinations of Higgs branch operators that can be inserted anywhere along a given line. These operators are constructed from the hypermultiplet scalars. They form a one-dimensional non-commutative operator algebra with topological correlation functions. The 2- and 3-point functions of Higgs branch operators in the full 3d ${\cal N}=4$ theory can be simply inferred from the 1d topological algebra. After conformally mapping the 3d superconformal field theory from flat space to a round three-sphere, we preform supersymmetric localization using a supercharge that does not belong to any 3d ${\cal N} = 2$ subalgebra of the ${\cal N}=4$ algebra. The result is a simple model that can be used to calculate correlation functions in the 1d topological algebra mentioned above. This model is a 1d Gaussian theory coupled to a matrix model, and it can be viewed as a gauge-fixed version of a topological gauged quantum mechanics. Our results generalize to non-conformal theories on $S^3$ that contain real mass and Fayet-Iliopolous parameters. We also provide partial results in the 1d topological algebra associated with the Coulomb branch, where we calculate correlation functions of local operators built from the vectormultiplet scalars.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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