The operator product expansion of the lowest higher spin current at finite N

Kim

Paeng

2016

Int. J. Mod. Phys. A

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We construct the lowest higher spin-2 current in terms of the spin-1 and the spin- Wolf space coset theory for general N. The remaining fifteen higher spin currents are determined. We obtain the three-point functions of bosonic (higher) spin currents with two scalars for finite N and k (the level of the spin-1 current). By multiplying SU(2) × U(1) into the above Wolf space coset theory, the other fifteen higher spin currents together with the above lowest higher spin-2 current are realized in the extension of the large N = 4 linear superconformal algebra. Similarly, the three-point functions of bosonic (higher) spin currents with two scalars for finite N and k are obtained. Under the large N 't Hooft limit, the two types of three-point functions in the nonlinear and linear versions coincide as in the unitary coset theory found previously.

Section: 11mentioning

confidence: 99%

“…This is one of the reasons why we are interested in this particular orthogonal coset theory. See also the description of [10,11,12] in different orthogonal coset theory.…”

Section: Introductionmentioning

confidence: 99%

Three-point functions in the 𝒩 = 4 orthogonal coset theory

Kim

Paeng

2016

Int. J. Mod. Phys. A

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“…So far, the supersymmetric versions of minimal model holography are described in the recent works [40,41,42,43,32,44,33,45,46,47,48,49,50]. In particular, it would be interesting to see whether the W B N−1 2 minimal model can be generalized to the supersymmetric extension or not.…”

Section: Discussionmentioning

confidence: 99%

“…7 We have checked the OPE (3.2) when N = 6 and realize that the result is exactly the same as ( Then the OPE (3.2) under the large (N, k) limit can be obtained by substituting (3.12) and (3.13) into (3.2). See also the related works [32,33] where the large (N, k) 't Hooft limit on the OPE was described.…”

mentioning

confidence: 99%

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

Paeng²

2013

Class. Quantum Grav.

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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.

“…How does one determine other higher spin currents related to the lowest one? Let us recall that the following OPE [44,45,46]…”

mentioning

confidence: 99%

Higher spin currents in the orthogonal coset theory

2017

Eur. Phys. J. C

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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.