In this talk, I’m going to talk about the old questions regarding the classifications of gapped phases of 4d gauge theories from the modern viewpoint. Gauge theories not only provide the fundamental formulations of our worlds in particle physics but also give effective descriptions of various topological phases of matters in condensed-matter physics. In both perspectives, it is important to understand the quantum phases of their ground-state structures. Conventionally, this has been achieved by the so-called Wilson-’t Hooft classifications for 4d SU(N) gauge theories, and I will give its modern interpretation from SSB (spontaneous symmetry breaking) and SPT (symmetry-protected topological) states with the global 1-form symmetry.
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