Higher spin currents in the enhanced N = 3 $$ \mathcal{N}=3 $$ Kazama-Suzuki model

2021

J. High Energ. Phys.

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In the Grassmannian-like coset model, $$ \frac{\mathrm{SU}{\left(N+M\right)}_k}{\mathrm{SU}{(N)}_k\times \mathrm{U}{(1)}_{kNM\left(N+M\right)}} $$ SU N + M k SU N k × U 1 kNM 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 MM matrix generalization of AdS3 higher spin theory. Moreover, the OPE between the charged spin-3 current and itself is determined for fixed (N, M) = (5, 4) with arbitrary k up to the third order pole. We also obtain the OPEs between charged spin-1, 2, 3 currents and neutral spin-3 current. From the last OPE, we realize that there exists the presence of the above charged quasi primary spin-4 current in the second order pole for fixed (N, M) = (5, 4). We comment on the complex free fermion realization.

Section: Discussionmentioning

confidence: 99%

The Grassmannian-like coset model and the higher spin currents

2021

J. High Energ. Phys.

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“…2 Taking adjoint spin- 1 2 fermions in the second factor appearing in the numerator of the diagonal coset model [1] provides the coset construction for N = 2 superconformal algebra [12], and the observed N = 2 higher spin currents can be determined [13,14]. Creutzig et al and Ahn et al [15,16] investigated the N = 3 extension from the N = 2 coset model.…”

Section: Jhep05(2019)135mentioning

confidence: 99%

“…Let us consider the most general spin- 3 2 current with unknown U(1) charge q and unknown coefficients [16],…”

Section: Jhep05(2019)135mentioning

confidence: 99%

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

Paeng

2019

J. High Energ. Phys.

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By studying the N = 1 holographic minimal model at the "critical" level, we obtain the lowest N = 2 higher spin multiplet of spins 3 2 , 2, 2, 5 2 in terms of two adjoint fermion types for generic N. We subsequently determine operator product expansions between the lowest and second lowest (N = 2) higher spin multiplet of spins 3, 7 2 , 7 2 , 4 , and the corresponding Vasiliev's oscillator formalism with matrix generalization on AdS 3 higher spin theory in the extension of OSp(2|2) superconformal algebra. Under the large N limit (equivalent to large central charge) in the extension of N = 2 superconformal algebra in two dimensions, operator product expansions provide asymptotic symmetry algebra in AdS 3 higher spin theory.

“…It would be interesting to see whether there exist other additional higher spin currents or not. See also the work in [39] where the Jacobi identities are used.…”

Section: The Opes Between the Higher Spin 7 2 4 Currentsmentioning

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.