Abstract
We extend the definition of Lüscher’s lattice topological charge to the case of 4d SU(N) gauge fields coupled with ℤN 2-form gauge fields. This result is achieved while maintaining the locality, the SU(N) gauge invariance, and ℤN 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 ℤN 1-form symmetry and the θ periodicity.
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Acknowledgments
The authors appreciate the conference “Lattice and continuum field theories 2022” (YITP-W-22-02) at Yukawa Institute for Theoretical Physics (YITP) in the last July. This work was partially supported by Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research Grant Numbers JP21J30003 (O.M.), JP20H01903 (H.S.), JP22H01218, and JP20K22350 (Y.T.). The work of Y.T. was supported by Center for Gravitational Physics and Quantum Information (CGPQI) at YITP.
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Abe, M., Morikawa, O., Onoda, S. et al. Topology of SU(N) lattice gauge theories coupled with ℤN 2-form gauge fields. J. High Energ. Phys. 2023, 118 (2023). https://doi.org/10.1007/JHEP08(2023)118
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DOI: https://doi.org/10.1007/JHEP08(2023)118