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

Abstract

We compute the operator product expansion (OPE) between the spin-4 current and itself in the W D 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 W D 4 coset minimal model. Based on this N = 8 result, we generalize the above OPE for the general N(in the W D 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 W B 3 (and W B 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.

The operator product expansion between the 16 lowest higher spin currents in the $$\mathcal{N}=4$$ N = 4 superspace

“…Note that the lowest 16 higher spin currents have the lowest higher spin-2 current, whose OPE is nontrivial, compared to the corresponding higher spin-1 current for the unitary case, because the second-order pole contains the nontrivial composite spin-2 fields. In this direction, the work of [33][34][35][36][37] will be useful.…”

The next 16 higher spin currents and three-point functions in the large $$\mathcal{N}=4$$ N = 4 holography

“…It is straightforward to apply the work of [6] and the presentation of this paper to the orthogonal case [54] in the context of [55][56][57][58][59]. The lowest 16 higher spin currents contains the higher spin 2 current as its lowest component.…”

Higher spin currents with manifest SO(4) symmetry in the large 𝒩 = 4 holography

“…From the eigenvalues (−4, −8, −12) appearing in the fifth term for N = 3, 5, 7, the general N behavior is given by (−2N + 2). From the eigenvalues (16,32,48) appearing in the last term for N = 3, 5, 7, the general N behavior is given by (8N − 8).…”

“…The completely symmetric SO(2N) invariant tensor of rank-4 played an important role. See also the relevant papers in [15,16]. The N = 1 supersymmetric (higher spin currents) extension of the GKO coset construction in [7,8] has been studied in [17,18] by considering some condition for one of the levels of the coset model, which allows us to construct the fermionic spin-3 2 current, the superpartner of spin-2 stress energy tensor current (and the superpartners of bosonic higher spin currents) using a fermion field, along the line of [19,20].…”