2022/08/25 by Putrov, Pavel
#Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th) #Number Theory (math.NT) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2208.12071
We summarize basic features of quantum field theories with discrete symmetry ℚ/ℤ (possibly higher form, global or gauged). The classification of representations and anomalies is quite rich and involves the ring of profinite integers. As a main example we consider in detail 3d topological Dijkgraaf-Witten ℚ/ℤ gauge theories. We also briefly discuss relevance for some previously considered physical systems. In particular we comment on a relation to the recently discovered non-invertible symmetry in 4d QED and the problem of categorification of Chern-Simons TQFT.