Abstract
We consider the SU(N) Yang-Mills theory, whose topological sectors are restricted to the instanton number with integer multiples of p. We can formulate such a quantum field theory maintaining locality and unitarity, and the model contains both 2π-periodic scalar and 3-form gauge fields. This can be interpreted as coupling a topological theory to Yang-Mills theory, so the local dynamics becomes identical with that of pure Yang-Mills theory. The theory has not only ℤN 1-form symmetry but also ℤp 3-form symmetry, and we study the global nature of this theory from the recent ’t Hooft anomaly matching. The computation of ’t Hooft anomaly incorporates an intriguing higher-group structure. We also carefully examine that how such kinematical constraint is realized in the dynamics by using the large-N and also the reliable semiclassics on ℝ3 × S1, and we find that the topological susceptibility plays a role of the order parameter for the ℤp 3-form symmetry. Introducing a fermion in the fundamental or adjoint representation, we find that the chiral symmetry becomes larger than the usual case by ℤp, and it leads to the extra p vacua by discrete chiral symmetry breaking. No dynamical domain wall can interpolate those extra vacua since such objects must be charged under the 3-form symmetry in order to match the ’t Hooft anomaly.
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Tanizaki, Y., Ünsal, M. Modified instanton sum in QCD and higher-groups. J. High Energ. Phys. 2020, 123 (2020). https://doi.org/10.1007/JHEP03(2020)123
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DOI: https://doi.org/10.1007/JHEP03(2020)123