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Charting The Space Of 3d Cfts With A Continuous Global Symmetry, Anatoly Dymarsky, Joao Penedones, Emilio Trevisani, Alessandro Vichi

Physics and Astronomy Faculty Publications

We study correlation functions of a conserved spin-1 current J_μ in three dimensional Conformal Field Theories (CFTs). We investigate the constraints imposed by permutation symmetry and current conservation on the form of three point functions ⟨J_μJ_νO_Δ,ℓ⟩ and the four point function ⟨J_μJ_νJ_ρJ_σ⟩ and identify the minimal set of independent crossing symmetry conditions. We obtain a recurrence relation for conformal blocks for generic spin-1 operators in three dimensions. In the process, we improve several technical points, facilitating the use of recurrence relations. By applying …