论文标题
SU的椭圆形位点（3）真空
Elliptic Loci of SU(3) Vacua
论文作者
论文摘要
许多四维，$ \ Mathcal {n} = 2 $ supersymmetric量规理论的真空空间可以用复杂曲线的家族来鉴定。对于量规组$ su（2）$，就椭圆曲线和相关的模块化基本域而言，这给出了对低能量有效理论的完全明确描述。量规组$ su（3）真空吸尘器的二维空间参与了两个属属的复杂家族。我们使用所谓的Rosenhain形式为这些曲线分析了这个家庭。我们证明了$ su（3）$ vacua空间的两个天然一维subloci，$ \ mathcal {e} _u $和$ \ nathcal {e} _v $，每个都参数化椭圆曲线的家族。对于这些椭圆基因座，我们明确描述了顺序参数和基本域。基因座$ \ Mathcal {E} _U $包含相互局部对起的点，是经典一致性子组的基本领域。此外，基因座$ \ Mathcal {e} _v $包含超级符合的Argyres-Douglas点，并且是Fricke组的基本领域。
The space of vacua of many four-dimensional, $\mathcal{N}=2$ supersymmetric gauge theories can famously be identified with a family of complex curves. For gauge group $SU(2)$, this gives a fully explicit description of the low-energy effective theory in terms of an elliptic curve and associated modular fundamental domain. The two-dimensional space of vacua for gauge group $SU(3)$ parametrizes an intricate family of genus two curves. We analyze this family using the so-called Rosenhain form for these curves. We demonstrate that two natural one-dimensional subloci of the space of $SU(3)$ vacua, $\mathcal{E}_u$ and $\mathcal{E}_v$, each parametrize a family of elliptic curves. For these elliptic loci, we describe the order parameters and fundamental domains explicitly. The locus $\mathcal{E}_u$ contains the points where mutually local dyons become massless, and is a fundamental domain for a classical congruence subgroup. Moreover, the locus $\mathcal{E}_v$ contains the superconformal Argyres-Douglas points, and is a fundamental domain for a Fricke group.
