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arXiv · 2303.10977

Topology of $SU(N)$ lattice gauge theories coupled with $\mathbb{Z}_N$ $2$-form gauge fields

Motokazu Abe·Okuto Morikawa·Soma Onoda·Hiroshi Suzuki·Yuya Tanizaki
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Abstract

We extend the definition of L\"uscher's lattice topological charge to the case of $4$d $SU(N)$ gauge fields coupled with $\mathbb{Z}_N$ $2$-form gauge fields. This result is achieved while maintaining the locality, the $SU(N)$ gauge invariance, and $\mathbb{Z}_N$ $1$-form gauge invariance, and we find that the manifest $1$-form gauge invariance plays the central role in our construction. This result gives the lattice regularized derivation of the mixed 't Hooft anomaly in pure $SU(N)$ Yang-Mills theory between its $\mathbb{Z}_N$ $1$-form symmetry and the $\theta$ periodicity.

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Motokazu Abe, Okuto Morikawa, Soma Onoda, Hiroshi Suzuki, Yuya Tanizaki. 2023-03-20. Topology of $SU(N)$ lattice gauge theories coupled with $\mathbb{Z}_N$ $2$-form gauge fields. https://doi.org/10.1007/jhep08(2023)118

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