The OPEs of spin-4 Casimir currents in the holographic SO(N) coset minimal models

The operator product expansion (OPE) between the spin-4 current and itself in the WD₄ coset minimal model was calculated using SO(8) current algebra. The right-hand side of this OPE contains the spin-6 Casimir current, which is also a generator of the WD₄ coset minimal model. Based on this N = 8 result, the above OPE was generalized for the general N (in the coset minimal model) using the two N-generalized coupling constants initiated by Hornfeck, which is the simplest OPE for the lowest higher spin currents. The similar OPE in the WB₃ (and ) coset minimal model was also analyzed with the SO(7) current algebra. The large N 't Hooft limits are discussed. The results in two-dimensional conformal field theory provide asymptotic symmetry at the quantum level of the higher spin AdS₃ gravity reported by Chen et al.