Explicit Construction of Spin 4 Casimir Operator in the Coset Model $ \hat{SO} (5)_{1} \times \hat{SO} (5)_{m} / \hat{SO} (5)_{1+m} $

Abstract

We generalize the Goddard-Kent-Olive (GKO) coset construction to the dimension 5/2 operator for $ \hat{so} (5) $ and compute the fourth order Casimir invariant in the coset model $\hat{SO} (5)_{1} \times \hat{SO} (5)_{m} / \hat{SO} (5)_{1+m} $ with the generic unitary minimal $ c < 5/2 $ series that can be viewed as perturbations of the $ m \rightarrow \infty $ limit, which has been investigated previously in the realization of $ c= 5/2 $ free fermion model.