论文标题
Seiberg-Witten几何形状，模块化有理椭圆形表面和BPS颤动
Seiberg-Witten geometry, modular rational elliptic surfaces and BPS quivers
论文作者
论文摘要
我们研究等级的4D $ \ MATHCAL {n} = 2 $量子场理论的库仑分支，包括从5D $ \ MATHCAL {N} = 1 $ $ E_N $ SEIBERG的圆圈压实获得的KK理论。重点是将其Seiberg-witten几何形状与理性椭圆表面之间的关系设置为对模块化表面的更多关注，我们使用模块化组$ {\ rm psl}的子组的分类完全对此进行了分类（2，\ Mathbb {Z}）$。我们为所有一致性以及与这些几何形状相关的一些非统一亚组得出了模块化函数的闭合形式表达式。此外，我们展示了这些理论的BPS颤动如何直接从单构群的基本领域确定，并研究如何将这些域的变化解释为Quiver突变。这种方法还可以推广到其库仑分支中包含“不可辨别”奇异性的理论，从而导致了这种理论的已知纪念。
We study the Coulomb branches of the rank-one 4d $\mathcal{N} = 2$ quantum field theories, including the KK theories obtained from the circle compactification of the 5d $\mathcal{N}= 1$ $E_n$ Seiberg theories. The focus is set on the relation between their Seiberg-Witten geometries and rational elliptic surfaces, with more attention being given to the modular surfaces, which we completely classify using the classification of subgroups of the modular group ${\rm PSL}(2,\mathbb{Z})$. We derive closed-form expressions for the modular functions for all congruence and some of the non-congruence subgroups associated with these geometries. Moreover, we show how the BPS quivers of these theories can be determined directly from the fundamental domains of the monodromy groups and study how changes of these domains can be interpreted as quiver mutations. This approach can also be generalized to theories whose Coulomb branches contain `undeformable' singularities, leading to known quivers of such theories.
