Speaker
Description
Since Gaiotto et.~al discussed the low-energy dynamics of gauge theories on the basis of the mixed ’t Hooft anomaly between discrete and higher-form symmetries, this type of application of the anomaly has been studied vigorously. In this study, in order to understand this type of application of the anomaly in a completely regularized framework, we formulate the fractional topological charge associated with the $U(1)/\mathbb{Z}_q$ principal bundle in the compact $U(1)$ lattice gauge theory by generalizing L\“uscher’s construction. This fractional topological charge in lattice gauge theory is $\mathbb{Z}_q$ one-form gauge invariant and odd under the lattice time reversal transformation. By employing these properties of the fractional topological charge, we can show that the $U(1)$ gauge theory containing matter fields with charge $q\in 2\mathbb{Z}$ has the mixed ’t Hooft anomaly between the $\mathbb{Z}_q$ one-form symmetry and the time reversal symmetry when $\theta=\pi$. This is analogous to the mixed ’t Hooft anomaly between the $\mathbb{Z}_N$ one-form symmetry and the time reversal symmetry in $SU(N)/\mathbb{Z}_N$ theory when $\theta=\pi$.
