编织物、墙壁和镜子
Braids, Walls, and Mirrors
摘要：
通过考虑4d，N =2理论的单参数“R流”，我们构造了3d，N = 2超对称规范理论，其中中心荷在保持相序的同时发生变化. 4d中的每一个BPS态都导致3d中的一个BPS粒子，因此4d理论的每个腔室都导致一个不同的3d理论。通过壁交叉、R流与3d理论的镜像对相关的4d腔室对。特别地，A_2Argyres-Douglas理论的2-3壁交叉导致了Nf =1 SQED和XYZ模型的3d镜像对称性。虽然我们的形式主义适用于任意N=2的模型，我们专注于的情况下，父母4d理论由成对的M5膜包裹黎曼曲面，并开发一个通用的框架来描述3d N=2的理论工程包装对M5膜上的三个流形。每个4d腔室对应于双3d描述，映射到UV 3d几何形状的特定四面体分解。在IR中，物理学被单个重组的M5-膜捕获，它是原始UV三流形的分支双重覆盖。分支轨迹的编织和分支片的几何形状在编码物理过程中起着关键作用。
英文摘要：
We construct 3d, N=2 supersymmetric gauge theories by considering a one-parameter `R-flow' of 4d, N=2 theories, where the central charges vary while preserving their phase order. Each BPS state in 4d leads to a BPS particle in 3d, and thus each chamber of the 4d theory leads to a distinct 3d theory. Pairs of 4d chambers related by wall-crossing, R-flow to mirror pairs of 3d theories. In particular, the 2-3 wall-crossing for the A_2 Argyres-Douglas theory leads to 3d mirror symmetry for N_f=1 SQED and the XYZ model. Although our formalism applies to arbitrary N=2 models, we focus on the case where the parent 4d theory consists of pairs of M5-branes wrapping a Riemann surface, and develop a general framework for describing 3d N=2 theories engineered by wrapping pairs of M5-branes on three-manifolds. Each 4d chamber, which corresponds to a dual 3d description, maps to a particular tetrahedral decomposition of the UV 3d geometry. In the IR the physics is captured by a single recombined M5-brane which is a branched double cover of the original UV three-manifold. The braiding of branch loci and the geometry of branch sheets play a key role in encoding the physics.
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