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

Ahn, Changhyun; Paeng, Jinsub

doi:10.1007/jhep05(2019)135

Cited by 9 publications

(10 citation statements)

References 55 publications

(128 reference statements)

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“…Therefore, we are left with the above final result where there is no J c J u(1) f term. 29 In the last OPE of (6.2), there exist the following terms, after subtracting the descendant terms, which is a primary…”

Section: The Opes With the Second Componentmentioning

confidence: 99%

“…The question is whether this can be written in terms of the known currents or not. Let us look at t α ρ σ t b j ī t a l k t α μν ψ ( σ j) ψ (ρ ī) ψ ( νl) J (μ k) term appearing in the sixth line 29 For convenience, we present the OPEs J a (z)…”

Section: The Opes With the Second Componentmentioning

confidence: 99%

“…Without introducing the fermions, we can have the supersymmetric version of (1.1) by considering the special value of the level k. This is because we can realize the various spin-1 currents in terms of fermions. For example, see also[16][17][18][19][20][21][22][23][24][25][26][27][28][29] 4. The OPE between G + and G − does not produce the standard N = 2 superconformal algebra for generic M > 1 because the first order pole of this OPE has the additional terms.…”

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confidence: 99%

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Adding complex fermions to the Grassmannian-like coset model

Ahn

2021

Eur. Phys. J. C

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In the $${{\mathcal {N}}}=2$$ N = 2 supersymmetric coset model, $$\frac{SU(N+M)_k \times SO(2 N M)_1}{ SU(N)_{k+M} \times U(1)_{ N M (N+M)(k+N+M)}}$$ S U ( N + M ) k × S O ( 2 N M ) 1 S U ( N ) k + M × U ( 1 ) N M ( N + M ) ( k + N + M ) , we construct the SU(M) nonsinglet $${{\mathcal {N}}}=2$$ N = 2 multiplet of spins $$(1, \frac{3}{2}, \frac{3}{2}, 2)$$ ( 1 , 3 2 , 3 2 , 2 ) in terms of coset fields. The next SU(M) singlet and nonsinglet $${{\mathcal {N}}}=2$$ N = 2 multiplets of spins $$(2, \frac{5}{2}, \frac{5}{2}, 3)$$ ( 2 , 5 2 , 5 2 , 3 ) are determined by applying the $${{\mathcal {N}}}=2$$ N = 2 supersymmetry currents of spin $$\frac{3}{2}$$ 3 2 to the bosonic singlet and nonsinglet currents of spin 3 in the bosonic coset model. We also obtain the operator product expansions (OPEs) between the currents of the $${{\mathcal {N}}}=2$$ N = 2 superconformal algebra and above three kinds of $${{\mathcal {N}}}=2$$ N = 2 multiplets. These currents in two dimensions play the role of the asymptotic symmetry, as the generators of $${{\mathcal {N}}}=2$$ N = 2 “rectangular W-algebra”, of the $$M \times M$$ M × M matrix generalization of $$\mathcal{N}=2$$ N = 2 $$AdS_3$$ A d S 3 higher spin theory in the bulk. The structure constants in the right hand sides of these OPEs are dependent on the three parameters k, N and M explicitly. Moreover, the OPEs between SU(M) nonsinglet $${{\mathcal {N}}}=2$$ N = 2 multiplet of spins $$(1, \frac{3}{2}, \frac{3}{2}, 2)$$ ( 1 , 3 2 , 3 2 , 2 ) and itself are analyzed in detail. The complete OPE between the lowest component of the SU(M) singlet $${{\mathcal {N}}}=2$$ N = 2 multiplet of spins $$(2, \frac{5}{2}, \frac{5}{2}, 3)$$ ( 2 , 5 2 , 5 2 , 3 ) and itself is described. In particular, when $$M=2$$ M = 2 , it is known that the above $${{\mathcal {N}}}=2$$ N = 2 supersymmetric coset model provides the realization of the extension of the large $${{\mathcal {N}}}=4$$ N = 4 nonlinear superconformal algebra. We determine the currents of the large $${{\mathcal {N}}}=4$$ N = 4 nonlinear superconformal algebra and the higher spin-$$\frac{3}{2}, 2$$ 3 2 , 2 currents of the lowest $${{\mathcal {N}}}=4$$ N = 4 multiplet for generic k and N in terms of the coset fields. For the remaining higher spin-$$\frac{5}{2},3$$ 5 2 , 3 currents of the lowest $$\mathcal{N}=4$$ N = 4 multiplet, some of the results are given.

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Section: The Opes With the Second Componentmentioning

confidence: 99%

Section: The Opes With the Second Componentmentioning

confidence: 99%

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confidence: 99%

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Adding complex fermions to the Grassmannian-like coset model

Ahn

2021

Eur. Phys. J. C

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“…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.…”

Section: Review Of N = 4 Orthogonal Wolf Space Coset Modelmentioning

confidence: 99%

“…After that, we can go into the linear version (by changing the composite terms in the linear basis) together with the known field contents of the composite terms. 17 By decoupling of four spin- 1 2 currents and spin-1 current of the N = 4 linear superconformal algebra, we obtain the 11 currents of the N = 4 nonlinear superconformal algebra. The explicit expressions are given in (2.5).…”

Section: The Higher Spin Current Of Spinmentioning

confidence: 99%

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

2019

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Some of the operator product expansions (OPEs) between the lowest SO(4) singlet higher spin-2 multiplet of spins (2, 5 2 , 5 2 , 5 2 , 5 2 , 3, 3, 3, 3, 3, 3, 7 2 , 7 2 , 7 2 , 7 2 , 4) in an extension of the large N = 4 (non)linear superconformal algebra were constructed in the N = 4 superconformal coset SO(N +4) SO(N)×SO(4) theory with N = 4 previously. In this paper, by rewriting the above OPEs with N = 5, the remaining undetermined OPEs are completely determined. There exist additional SO(4) singlet higher spin-2 multiplet, six SO(4) adjoint higher spin-3 multiplets, four SO(4) vector higher spin-7 2 multiplets, SO(4) singlet higher spin-4 multiplet and four SO(4) vector higher spin-9 2 multiplets in the right hand side of these OPEs. Furthermore, by introducing the arbitrary coefficients in front of the composite fields in the right hand sides of the above complete 136 OPEs, the complete structures of the above OPEs are obtained by using various Jacobi identities for generic N. Finally, we describe them as one single N = 4 super OPE between the above lowest SO(4) singlet higher spin-2 multiplet in the N = 4 superspace.

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The $$ \mathcal{N} $$ = 4 higher spin algebra for generic μ parameter

Ahn

Kim

2021

J. High Energ. Phys.

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The $$ \mathcal{N} $$ N = 4 higher spin generators for general superspin s in terms of oscillators in the matrix generalization of AdS3 Vasiliev higher spin theory at nonzero μ (which is equivalent to the ’t Hooft-like coupling constant λ) were found previously. In this paper, by computing the (anti)commutators between these $$ \mathcal{N} $$ N = 4 higher spin generators for low spins s1 and s2 (s1 + s2 ≤ 11) explicitly, we determine the complete $$ \mathcal{N} $$ N = 4 higher spin algebra for generic μ. The three kinds of structure constants contain the linear combination of two different generalized hypergeometric functions. These structure constants remain the same under the transformation μ ↔ (1 − μ) up to signs. We have checked that the above $$ \mathcal{N} $$ N = 4 higher spin algebra contains the $$ \mathcal{N} $$ N = 2 higher spin algebra, as a subalgebra, found by Fradkin and Linetsky some time ago.

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

Cited by 9 publications

References 55 publications

Adding complex fermions to the Grassmannian-like coset model

Adding complex fermions to the Grassmannian-like coset model

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

The $$ \mathcal{N} $$ = 4 higher spin algebra for generic μ parameter

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