The OPEs of Spin-4 Casimir Currents in the Holographic SO(N) Coset Minimal Models

TL;DR

This paper computes and generalizes the operator product expansion of spin-4 currents in SO(N) coset minimal models, revealing their role as asymptotic symmetries in higher spin AdS_3 gravity.

Contribution

It provides explicit OPE calculations for spin-4 currents in WD_N/2 coset models and extends these results to general N, connecting conformal field theory with higher spin gravity.

Findings

Derived the OPE between spin-4 currents and itself in WD_4 coset models.

Generalized the OPE for arbitrary N using N-dependent coupling constants.

Discussed the large N 't Hooft limit and its implications for asymptotic symmetries.

Abstract

We compute the operator product expansion (OPE) between the spin-4 current and itself in the WD_4 coset minimal model with SO(8) current algebra. The right hand side of this OPE contains the spin-6 Casimir current which is also a generator of WD_4 coset minimal model. Based on this N=8 result, we generalize the above OPE for the general N(in the WD_{N/2} coset minimal model) by using two N-generalized coupling constants initiated by Hornfeck sometime ago: the simplest OPE for the lowest higher spin currents. We also analyze the similar OPE in the WB_3(and WB_{(N-1)/2}) coset minimal model with SO(7) current algebra. The large N 't Hooft limits are discussed. Our results in two dimensional conformal field theory provide the asymptotic symmetry, at the quantum level, of the higher spin AdS_3 gravity found by Chen et al.