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

Ahn, Changhyun

doi:10.1142/s0217751x18502081

Cited by 6 publications

(4 citation statements)

References 85 publications

(302 reference statements)

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“…In model building it has been used for extensions of the Standard Model in the way of BSM models [23,24,25,26,27,28,29], grand unified models [30,31,32,33,34,35,36,37,38,39,40,41,42,43], and other applications including SUSY models [44,45,46], supergravity models [47] and general particle physics models [48,49]. In UV completions of particle physics models, LieART has found uses in string theory [50,51], holography [52,53,54], (super-)conformal field theory [55,56,57,58,59,60,61,62,63], M-theory [64,65] and F-theory [66,67,68]. Beyond these applications LieART has been used in studying quantum groups [69,…”

Section: Examples Of Simplementioning

confidence: 99%

LieART 2.0 -- A Mathematica Application for Lie Algebras and Representation Theory

Feger,

Kephart,

Saskowski

2019

Preprint

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We present LieART 2.0 which contains substantial extensions to the Mathematica application LieART (Lie Algebras and Representation Theory) for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. The basic procedure is unchanged-it computes root systems of Lie algebras, weight systems and several other properties of irreducible representations, but new features and procedures have been included to allow the extensions to be seamless. The new version of LieART continues to be user friendly. New extended tables of properties, tensor products and branching rules of irreducible representations are included in the appendix for use without Mathematica software. LieART 2.0 now includes the branching rules to special subalgebras for all classical and exceptional Lie algebras up to and including rank 15.

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Section: Examples Of Simplementioning

confidence: 99%

LieART 2.0 -- A Mathematica Application for Lie Algebras and Representation Theory

Feger,

Kephart,

Saskowski

2019

Preprint

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“…For M = 2, the above coset arises in the context of the large N = 4 holography [46]. See also previous works on this holography [47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,2,70,71,72].…”

Section: Introductionmentioning

confidence: 81%

Adding Complex Fermions to the Grassmannian-like Coset Model

Ahn

2021

Preprint

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In the N = 2 supersymmetric coset model, SU (N +M ) k ×SO(2N M ) 1 SU (N ) k+M ×U (1) NM (N+M )(k+N+M ) , we construct the SU(M) nonsinglet N = 2 multiplet of spins (1, 3 2 , 3 2 , 2) in terms of coset fields. The next SU(M) singlet and nonsinglet N = 2 multiplets of spins (2, 5 2 , 5 2 , 3) are determined by applying the N = 2 supersymmetry currents of spin 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 N = 2 superconformal algebra and above three kinds of N = 2 multiplets. These currents in two dimensions play the role of the asymptotic symmetry, as the generators of N = 2 "rectangular W -algebra", of the M × M matrix generalization of N = 2 AdS 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 N = 2 multiplet of spins (1, 3 2 , 3 2 , 2) and itself are analyzed in detail. The complete OPE between the lowest component of the SU(M) singlet N = 2 multiplet of spins (2, 5 2 , 5 2 , 3) and itself is described. In particular, when M = 2, it is known that the above N = 2 supersymmetric coset model provides the realization of the extension of the large N = 4 nonlinear superconformal algebra. We determine the currents of the large N = 4 nonlinear superconformal algebra and the higher spin-3 2 , 2 currents of the lowest N = 4 multiplet for generic k and N in terms of the coset fields. For the remaining higher spin-5 2 , 3 currents of the lowest N = 4 multiplet, some of the results are given.7 Towards the OPEs between the singlet multiplet of spins (2, 5 2 , 5 2 , 3) and itself 8 The extension of the large N = 4 nonlinear superconformal algebra for M = 2 8.

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“…According to the results of this paper, there are many higher spin currents from the single OPE (4.25). It is an open problem to obtain the remaining 15 higher spin currents in terms of the orthogonal Wolf space coset fields explicitly and to calculate the eigenvalues of the zero modes, by following the procedure studied in [43][44][45][46][47]. Although this will be rather involved, once we obtain them, then it is straightforward to compute the three-point functions at finite N and k.…”

Section: Discussionmentioning

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

Cited by 6 publications

References 85 publications

LieART 2.0 -- A Mathematica Application for Lie Algebras and Representation Theory

LieART 2.0 -- A Mathematica Application for Lie Algebras and Representation Theory

Adding Complex Fermions to the Grassmannian-like Coset Model

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

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