论文标题
3D $ \ MATHCAL {n} = 4 $ SUSY GAUGE理论和海森伯格代数的超对称地面状态
Supersymmetric ground states of 3d $\mathcal{N}=4$ SUSY gauge theories and Heisenberg Algebras
论文作者
论文摘要
我们考虑3D $ \ MATHCAL {n} = 4 $几何理论$σ\ times \ times \ Mathbb {r} $，其中$σ$是从$ \ Mathbb {r} $上的量子机制的角度来看，$σ$是封闭且连接的riemann表面。在存在真实变形参数的情况下，集中在基本镜对上，即用一个超多年（SQED [1]）和自由的超孔集，我们研究了相应量子力学中本地操作员的代数，以及它们对它们对副基层状态的载体空间的作用。我们证明可以用海森堡代数来描述代数，并且它们以一种让人联想起Segal-Bargmann（自由超人的B-twist）和Nakajima（SQED [1]）操作员的方式的作用。
We consider 3d $\mathcal{N} = 4$ theories on the geometry $Σ\times\mathbb{R}$, where $Σ$ is a closed and connected Riemann surface, from the point of view of a quantum mechanics on $\mathbb{R}$. Focussing on the elementary mirror pair in the presence of real deformation parameters, namely SQED with one hypermultiplet (SQED[1]) and the free hypermulitplet, we study the algebras of local operators in the respective quantum mechanics as well as their action on the vector space of supersymmetric ground states. We demonstrate that the algebras can be described in terms of Heisenberg algebras, and that they act in a way reminiscent of Segal-Bargmann (B-twist of the free hypermultiplet) and Nakajima (A-twist of SQED[1]) operators.
