Higher spin currents in the orthogonal coset theory

Abstract

In the coset model (D (1)N ) at levels (k 1 , k 2 ), the higher spin 4 current that contains the quartic WZW currents contracted with a completely symmetric SO(2N ) invariant d tensor of rank 4 is obtained. The threepoint functions with two scalars are obtained for any finite N and k 2 with k 1 = 1. They are determined also in the large N 't Hooft limit. When one of the levels is the dual Coxeter number of SO(2N ), k 1 = 2N − 2, the higher spin 7 2 current, which contains the septic adjoint fermions contracted with the above d tensor and the triple product of structure constants, is obtained from the operator product expansion (OPE) between the spin 3 2 current living in the N = 1 superconformal algebra and the above higher spin 4 current. The OPEs between the higher spin 7 2 , 4 currents are described. For k 1 = k 2 = 2N − 2 where both levels are equal to the dual Coxeter number of SO(2N ), the higher spin 3 current of U (1) charge 4 3 , which contains the six products of spin 1 2 (two) adjoint fermions contracted with the product of the d tensor and two structure constants, is obtained. The corresponding N = 2 higher spin multiplet is determined by calculating the remaining higher spin 7 2 , 7 2 , 4 currents with the help of two spin 3 2 currents in the N = 2 superconformal algebra. The other N = 2 higher spin multiplet, whose U (1) charge is opposite to the one of the above N = 2 higher spin multiplet, is obtained. The OPE between these two N = 2 higher spin multiplets is also discussed.

A supersymmetric enhancement of $$ \mathcal{N} $$ = 1 holographic minimal model

“…Then we can generalize [17] by considering Klebanov and Polyakov duality in one lower dimension. The relevant coset model was derived by replacing the SU(N ) group by SO(2N ) or SO(2N + 1) [25,26], and N = 1 and N = 2 extensions of the (bosonic) orthogonal coset model obtained [27] (see [28] also). Thus, putting the above level condition into the N = 1 coset model, we can obtain the N = 2 extension of the supersymmetric coset model.…”

“…• Vasiliev's oscillator formalism with matrix generalization. It would be interesting to construct the Vasiliev's oscillator formalism in different coset models [10,11,14,16,27]. We can analyze the present method in the general coset model, e.g.…”

The operator product expansions in the $$\mathcal{N}=4$$ orthogonal Wolf space coset model

“…There are related works in [9][10][11]16] on this Wolf space coset model. There are also previous works on the orthogonal coset models in [17][18][19][20][21][22][23][24][25] along the line of [26][27][28]. 5 After we divide SU (2) × U (1) in the coset of [3], we obtain the Wolf space coset.…”

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

“…The three-point functions of the (bosonic) higher spin 1, 2, 3 currents (which are member of the above lowest 16 higher spin currents) both in the linear and nonlinear versions with two scalars have been found in [22]. One of the main features of this construction is that we do not have to obtain the explicit results for the higher spin currents in terms of WZW affine KacMoody currents for generic N (and k) manually where the bosonic spin 1 affine Kac-Moody current has the level k, contrary to the other cases where the complete results are needed [23][24][25][26][27][28][29][30] in the context of [31][32][33] except for the overall factor. That is, the lowest 16 higher spin currents in terms of affine Kac Moody currents for several N -values (N = 3, 5, 7, 9) are enough to determine the three-point functions even at finite N (and k).…”