论文标题
强耦合处的3D接口的几何方法
Geometric Approach to 3D Interfaces at Strong Coupling
论文作者
论文摘要
我们研究了4D系统，其中该理论的参数在一个空间方向上具有位置依赖性。在这些参数跳跃的极限中，这可能会导致支持本地化自由度的3D接口。先验，这种位置依赖性可以在弱耦合或强耦合下发生。 $ u（1）$级理论的苛刻时间逆转不变性，具有双重性$γ\ subset sl（2，\ mathbb {z}）$导致以强耦合为特征的接口，其特征在于$γ$ $γ$的模块化曲线的真实组件。这提供了一种几何方法，用于提取可能的局部状态的电荷和磁电荷。我们通过分析一些具有3D接口的4D $ \ MATHCAL {N} = 2 $理论来说明这些一般考虑。这些4D系统也可以解释为从六维理论中降低，该理论是在由真实线上纤维的Riemann表面家族产生的三个manifold上的。我们更普遍地表明，在此类空间上压缩的6D超符号场理论也通过在所得的4D块状理论中使用已知的异常结构来产生被捕获的物质。
We study 4D systems in which parameters of the theory have position dependence in one spatial direction. In the limit where these parameters jump, this can lead to 3D interfaces supporting localized degrees of freedom. A priori, this sort of position dependence can occur at either weak or strong coupling. Demanding time-reversal invariance for $U(1)$ gauge theories with a duality group $Γ\subset SL(2,\mathbb{Z})$ leads to interfaces at strong coupling which are characterized by the real component of a modular curve specified by $Γ$. This provides a geometric method for extracting the electric and magnetic charges of possible localized states. We illustrate these general considerations by analyzing some 4D $\mathcal{N} = 2$ theories with 3D interfaces. These 4D systems can also be interpreted as descending from a six-dimensional theory compactified on a three-manifold generated by a family of Riemann surfaces fibered over the real line. We show more generally that 6D superconformal field theories compactified on such spaces also produce trapped matter by using the known structure of anomalies in the resulting 4D bulk theories.
