论文标题
Cardy-Rabinovici模型和混合重力异常的不可逆转性自以为是的缺陷
Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly
论文作者
论文摘要
我们研究Cardy-Rabinovici模型中自偶性对称性的特性。 Cardy-Rabinovici模型是带有电气和磁性物质的$ 4 $ D $ U（1）$量规理论，它享受$ SL（2，\ Mathbb {z}）$ suff-Enfiality。 $SL(2,\mathbb{Z})$ self-duality does not realize in a naive way, but we notice that the $ST^{p}$ duality transformation becomes the legitimate duality operation by performing the gauging of $\mathbb{Z}_N$ $1$-form symmetry with including the level-$p$ discrete topological term.由于其实现的并发症，二元性缺陷的融合规则变成了一种非组样结构，因此自偶性对称性被实现为不可糊化的对称性。此外，对于自偶性的某些固定点，二元性对称性事实证明在$ k3 $表面上检测到混合的引力异常，由于异常匹配，我们可以排除微不足道的相位阶段。我们还揭示了Cardy-Rabinovici模型的猜想相图如何满足这种新的异常匹配条件。
We study properties of self-duality symmetry in the Cardy-Rabinovici model. The Cardy-Rabinovici model is the $4$d $U(1)$ gauge theory with electric and magnetic matters, and it enjoys the $SL(2,\mathbb{Z})$ self-duality at low-energies. $SL(2,\mathbb{Z})$ self-duality does not realize in a naive way, but we notice that the $ST^{p}$ duality transformation becomes the legitimate duality operation by performing the gauging of $\mathbb{Z}_N$ $1$-form symmetry with including the level-$p$ discrete topological term. Due to such complications in its realization, the fusion rule of duality defects becomes a non-group-like structure, and thus the self-duality symmetry is realized as a non-invertible symmetry. Moreover, for some fixed points of the self-duality, the duality symmetry turns out to have a mixed gravitational anomaly detected on a $K3$ surface, and we can rule out the trivially gapped phase as a consequence of anomaly matching. We also uncover how the conjectured phase diagram of the Cardy-Rabinovici model satisfies this new anomaly matching condition.
