The Grassmannian-like Coset Model and the Higher Spin Currents

Understand

In the Grassmannian-like coset model, $\frac{SU(N+M)_k}{SU(N)_k \times U(1)_{k N M (N+M)}}$, Creutzig and Hikida have found the charged spin-$2,3$ currents and the neutral spin-$2,3$ currents previously.

• In this paper, as an extension of Gaberdiel-Gopakumar conjecture found ten years ago, we calculate the operator product expansion (OPE) between the charged spin-$2$ current and itself, the OPE between the charged spin-$2$ current and the charged spin-$3$ current and the OPE between the neutral spin-$3$ current and itself for generic $N, M$ and $k$.
• From the second OPE, we obtain the new charged quasi primary spin-$4$ current while from the last one, the new neutral primary spin-$4$ current is found implicitly.
• The infinity limit of $k$ in the structure constants of the OPEs is described in the context of asymptotic symmetry of $M \times M$ matrix generalization of $AdS_3$ higher spin theory.