arXiv 2406.092612024-06hep-th

通过半时空规范得到的2+1维量子场论中的不可逆表面缺陷

Non-Invertible Surface Defects in 2+1d QFTs from Half Spacetime Gauging

Wei Cui, Babak Haghighat, Lorenzo Ruggeri

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AI总结：

该研究针对2+1维具有特定整体对称性和反常的量子场论，通过半时空规范定义对偶缺陷，推导其融合规则、构造对称拓扑场论，并在规范理论及非拉格朗日理论中给出实例。

摘要：

我们研究具有$\bZ^{(0)}_N\times\bZ^{(1)}_N$整体对称性和平凡混合't Hooft反常的2+1维理论中的对偶缺陷。通过在半时空同时规范这些对称性，我们为在规范下自对偶的理论定义了对偶缺陷。我们计算了涉及对偶缺陷的融合规则，并表明它们服从融合2-范畴。我们还构造了相应的对称拓扑场论，即平板上的四维BF理论，其在收缩区间时可在边界上实现对偶缺陷。此外，我们在$U(1)\times U(1)$规范理论和更一般的乘积理论中提供了此类对偶缺陷的明确例子。最后，我们在通过将6维$\frak{N}=(2,0)$型$A_{N-1}$超共形场论在各种三维流形上紧致化得到的非拉格朗日理论中找到了对偶缺陷。

英文摘要：

We study duality defects in 2+1d theories with $\bZ^{(0)}_N\times\bZ^{(1)}_N$ global symmetry and trivial mixed 't Hooft anomaly. By gauging these symmetries simultaneously in half of the spacetime, we define duality defects for theories that are self-dual under gauging. We calculate the fusion rules involving duality defects and show that they obey a fusion 2-category. We also construct the corresponding symmetry topological field theory, a four-dimensional BF theory on a slab which realizes the duality defects on the boundary upon shrinking the interval. Furthermore, we provide explicit examples of such duality defects in $U(1)\times U(1)$ gauge theories and in more general product theories. Finally, we find duality defects in non-Lagrangian theories obtained by compactification of 6d $\cN=(2,0)$ SCFTs of type $A_{N-1}$ on various three-manifolds.

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