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

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arxiv 2303.10977 v2 pith:QBLDAH4T submitted 2023-03-20 hep-lat hep-th

Motokazu Abe , Okuto Morikawa , Soma Onoda , Hiroshi Suzuki , Yuya Tanizaki This is my paper · ORCID
classification hep-lathep-th
keywords gaugeformmathbbfieldsinvariancelatticecoupledresult
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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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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Direct Monte Carlo Computation of the 't~Hooft Partition Function

    hep-lat 2025-01 conditional novelty 7.0 of 10

    A direct Monte Carlo count of 't Hooft flux sectors yields the 't Hooft partition function for SU(2) Yang-Mills, confirming the ordinary confining phase and, via the Witten effect, indicating oblique confinement at theta=2pi.

  2. Monte Carlo Simulation of the $SU(2)/\mathbb{Z}_2$ Yang--Mills Theory

    hep-lat 2024-12 conditional novelty 7.0 of 10

    Making the Z2 two-form gauge field dynamical in an SU(2)/Z2 lattice simulation shortens the autocorrelation time of the topological charge and of a gradient-flow energy observable compared with conventional SU(2) HMC.

  3. Confinement as Decoding: Higher Form Codes and Lattice Yang-Mills Theory

    hep-th 2026-08 conditional novelty 6.0 of 10

    Decoding a higher-form quantum code with Wilson-line noise is the same computation as comparing center-twisted Yang-Mills partition functions; the paper works out this dictionary and its strong-coupling consequences.

  4. Numerical simulation of fractional topological charge in $SU(N)$ gauge theory coupled with $\mathbb{Z}_N$ 2-form gauge fields

    hep-lat 2025-01 conditional novelty 5.0 of 10

    Numerical lattice simulation confirms that Z_2 2-form gauge-field coupling produces fractional (half-integer) topological charge in SU(2) gauge theory and reduces topological autocorrelation.

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