论文标题
自上而下的拓扑二元性缺陷
Top Down Approach to Topological Duality Defects
论文作者
论文摘要
拓扑二元性缺陷作为量子场理论（QFTS）中的一个通用对称算子出现，具有对称性对称性。最近的调查表明，在4D $ \ Mathcal {n} = 4 $ Super Yang-Mills（Sym）理论中，适当的选择（复杂的）量规耦合和量规组的全球形式可以导致相当丰富的融合代数用于相关的缺陷，从而导致了不可固化的对称性的示例。在这项工作中，我们呈现了这些双重性缺陷的自上而下结构，这些缺陷将概括为较低的超对称性QFT，而其他0形式的对称性通常存在。我们通过D3-Branes探测了$ x $ x $ a calabi-yau三倍圆锥，并在圆锥尖端上孤立的奇异性，我们意识到了QFT。 IIB二元组降为4D Worldvolume理论的二元性。非平凡的编纂一个拓扑接口是由7个Branes“ in Infinity”的配置产生的，该配置实现了合适的$ SL（2，\ Mathbb {Z}）$转换时。减少边界拓扑$ \ partial x $导致5D对称性TFT。对偶性缺陷的不同实现，例如使用某些混合异常和半空间测量结构的1形式对称性的测量，只是等于将分支切割在5D块中的不同选择。
Topological duality defects arise as codimension one generalized symmetry operators in quantum field theories (QFTs) with a duality symmetry. Recent investigations have shown that in the case of 4D $\mathcal{N} = 4$ Super Yang-Mills (SYM) theory, an appropriate choice of (complexified) gauge coupling and global form of the gauge group can lead to a rather rich fusion algebra for the associated defects, leading to examples of non-invertible symmetries. In this work we present a top down construction of these duality defects which generalizes to QFTs with lower supersymmetry, where other 0-form symmetries are often present. We realize the QFTs of interest via D3-branes probing $X$ a Calabi-Yau threefold cone with an isolated singularity at the tip of the cone. The IIB duality group descends to dualities of the 4D worldvolume theory. Non-trivial codimension one topological interfaces arise from configurations of 7-branes "at infinity" which implement a suitable $SL(2, \mathbb{Z})$ transformation when they are crossed. Reduction on the boundary topology $\partial X$ results in a 5D symmetry TFT. Different realizations of duality defects, such as the gauging of 1-form symmetries with certain mixed anomalies and half-space gauging constructions, simply amount to distinct choices of where to place the branch cuts in the 5D bulk.
