2022/12/08 by Arias-Tamargo, Guillermo, Benvenuti, Sergio, Rodriguez-Gomez, Diego · 1 citation
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2212.04427
We compute anomalous dimensions of quartic operators which are singlets under the U(Nf) global symmetry in Yang-Mills theories with Chern-Simons level k in three dimensions coupled to Nf Dirac fermions. In order to have analytic control, we consider the regime Nf≫ Nc≫ 1, where the problem is reduced to the study of a flavor-adjoint and a flavor-singlet bilinears whose square give the quartic operators of interest. We provide evidence that these operators hit marginality, signaling instabilities which, for (2k)/(Nf)<1 suggest the spontaneous breaking of the global symmetry, and no symmetry breaking otherwise. For k=Nf/2-1 (the value corresponding to the domain walls of 4d QCD at θ=π), the critical value Nf^* is tantalizingly close to the lower end of the conformal window of QCD4, suggesting a connection between conformal and global symmetry breaking in the 4d theory and in its domain walls. We also study, at k=0, other quartic operators containing a singlet when branched under U((Nf)/(2))× U((Nf)/(2)), finding that they hit marginality precisely at the same point as their flavor-neutral cousins. Using the same technology we study bosonic CS-QCD3, finding no hint of symmetry breaking where our analysis is applicable.