论文标题
3+1维度的不可变性凝结，二元性和试验性缺陷
Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions
论文作者
论文摘要
我们讨论了各种包含一个不可变形的拓扑缺陷，通常3+1D QFT，具有离散的一式全局对称性。这些包括来自较高的condemitions对称对称性的凝结缺陷，每个形式的对称性歧管上的歧管，每个歧管都以离散的扭转类标记，二元性和试验性缺陷来自时间的一半时间。确定了这些不可变形的拓扑缺陷与一形对称表面缺陷之间的通用融合规则。有趣的是，融合系数通常不是数字，而是2+1D TQFT，例如可逆SPT阶段，$ \ Mathbb {z} _n $ gauge理论和$ u（1）_N $ CHERN-SIMONS。这些代数对TQFT系数的关联依赖于大约2+1D TQFT的非平凡事实。我们进一步证明，其中一些不可逆转的对称性与琐碎的阶段本质上不相容，从而导致对重新归一化组流的非平凡约束。二元性和试验性缺陷在许多熟悉的仪表理论中都实现，包括免费的麦克斯韦理论，具有正交量规组的非亚洲仪表理论，$ {\ cal n} = 1，$和$ {\ cal n} = 4 $ super yang-super yang-yang-mills理论。
We discuss a variety of codimension-one, non-invertible topological defects in general 3+1d QFTs with a discrete one-form global symmetry. These include condensation defects from higher gauging of the one-form symmetries on a codimension-one manifold, each labeled by a discrete torsion class, and duality and triality defects from gauging in half of spacetime. The universal fusion rules between these non-invertible topological defects and the one-form symmetry surface defects are determined. Interestingly, the fusion coefficients are generally not numbers, but 2+1d TQFTs, such as invertible SPT phases, $\mathbb{Z}_N$ gauge theories, and $U(1)_N$ Chern-Simons theories. The associativity of these algebras over TQFT coefficients relies on nontrivial facts about 2+1d TQFTs. We further prove that some of these non-invertible symmetries are intrinsically incompatible with a trivially gapped phase, leading to nontrivial constraints on renormalization group flows. Duality and triality defects are realized in many familiar gauge theories, including free Maxwell theory, non-abelian gauge theories with orthogonal gauge groups, ${\cal N}=1,$ and ${\cal N}=4$ super Yang-Mills theories.
