论文标题
$ \ mathcal {n} = 1 $ super-yang-mills的矩阵模型的bort-oppenheimer量化
Born-Oppenheimer Quantization of the Matrix Model for $\mathcal{N}=1$ super-Yang-Mills
论文作者
论文摘要
我们构建了一个量子机械矩阵模型，该模型近似于$ \ mathcal {n} = 1 $ super-yang-mills $ s^3 \ times \ times \ mathbb {r} $。我们这样做是通过将量规捆绑包的一组左右连接撤回到真实的超空间中，并使用空间$ \ mathbb {r}^3 $压实到$ s^3 $。我们使用Born-oppenheimer近似量化了$ \ Mathcal {n} = 1 $ $ $ $ $ $ $ $ $ SU（2）$矩阵模型，并发现在该策略中出现了有效的Gluon动力学，以想起整个量子理论的不同阶段。我们证明，尽管有微妙的方式，但oppenheimer量化确实与超对称性兼容。实际上，我们可以定义有效的增压，以将矩阵模型的Hilbert Space的不同扇区相关联。这些有效的增压在理论的每个阶段都有不同的定义。
We construct a quantum mechanical matrix model that approximates $\mathcal{N}=1$ super-Yang-Mills on $S^3\times\mathbb{R}$. We do so by pulling back the set of left-invariant connections of the gauge bundle onto the real superspace, with the spatial $\mathbb{R}^3$ compactified to $S^3$. We quantize the $\mathcal{N}=1$ $SU(2)$ matrix model in the weak-coupling limit using the Born-Oppenheimer approximation and find that different superselection sectors emerge for the effective gluon dynamics in this regime, reminiscent of different phases of the full quantum theory. We demonstrate that the Born-Oppenheimer quantization is indeed compatible with supersymmetry, albeit in a subtle manner. In fact, we can define effective supercharges that relate the different sectors of the matrix model's Hilbert space. These effective supercharges have a different definition in each phase of the theory.
