Higher spin currents in orthogonal Wolf space

Ahn, Changhyun; Paeng, Jinsub

doi:10.1088/0264-9381/32/4/045011

Cited by 21 publications

(39 citation statements)

References 105 publications

(536 reference statements)

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“…So far the higher spin extension of the large N = 4 nonlinear superconformal algebra in the realization of large N = 4 orthogonal coset theory was obtained in [32]. It is straightforward to construct the is given by…”

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confidence: 99%

The operator product expansion between the 16 lowest higher spin currents in the $$\mathcal{N}=4$$ N = 4 superspace

Ahn

Kim

2016

Eur. Phys. J. C

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Some of the operator product expansions (OPEs) between the lowest 16 higher spin currents of spins (1, (5) SU(3) theory previously. In this paper, by rewriting these OPEs in the N = 4 superspace developed by Schoutens (and other groups), the remaining undetermined OPEs in which the corresponding singular terms possess the composite fields with spins s = 7 2 , 4, 9 2 , 5 are completely determined. Furthermore, by introducing arbitrary coefficients in front of the composite fields on the right-hand sides of the above complete 136 OPEs, reexpressing them in the N = 2 superspace, and using the N = 2 OPEs Mathematica package by Krivonos and Thielemans, the complete structures of the above OPEs with fixed coefficient functions are obtained with the help of various Jacobi identities. We then obtain ten N = 2 super OPEs between the four N = 2 higher spin currents denoted by (1,

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confidence: 99%

The operator product expansion between the 16 lowest higher spin currents in the $$\mathcal{N}=4$$ N = 4 superspace

Ahn

Kim

2016

Eur. Phys. J. C

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“…It is straightforward to apply the work of [6] and the presentation of this paper to the orthogonal case [54] in the context of [55][56][57][58][59]. The lowest 16 higher spin currents contains the higher spin 2 current as its lowest component.…”

Section: Discussionmentioning

confidence: 98%

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

Ahn

Kim

2017

Eur. Phys. J. C

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“…Higher spin representations have been considered in recent years in the context of string theory, investigations of the matter spectrum, and Clifford analysis [58,59,60,61,62,63,64,65,66,67] and they are therefore of special interest. With respect to higher spin note that degree n-polynomials in z ∈ C form the carrier module for the n + 1-dimensional irreducible spin representation of SU (2, C) [39].…”

Section: Higher Spinmentioning

confidence: 99%

Holographic coordinates

Ulrych¹

2018

Journal of Mathematical Analysis and Applications

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The Laplace equation in the two-dimensional Euclidean plane is considered in the context of the inverse stereographic projection. The Lie algebra of the conformal group as the symmetry group of the Laplace equation can be represented solely in terms of the solutions and derivatives of the solutions of the Laplace equation. It is then possible to put contents from differential geometry and quantum systems, like the Hopf bundle, relativistic spin, bicomplex numbers, and the Fock space into a common context. The basis elements of the complex numbers, considered as a Clifford paravector algebra, are reinterpreted as differential tangent vectors referring to dilations and rotations. In relation to this a homogeneous space is defined with the Lie algebra of the conformal group, where dilations and rotations are the coset representatives. Potential applications in physics are discussed. et al. [25]. Furthermore, a hierarchy of projective geometric spaces and Möbius geometries can be introduced based on Vahlen matrices [26,27,28,29]. Maks [30] investigated explicitly the sequence of Möbius geometries represented in terms of Clifford algebras, which is considered also in [31] in a bicomplex matrix representation. In relation to particle physics one may assume that projections of a more general geometry can arise as part of the measurement process via electromagnetic forces. In accordance with the holographic principle Möbius geometries and Möbius transformations can provide here a new perspective on the experimental data.Atiyah, Manton, and Schroers [32,33,34,35] describe electrons, protons, neutrinos, and neutrons within a model that has been inspired by Skyrme's baryon theory [36]. The Skyrme model became popular when Witten came up with the idea that baryons arise as solitons of the classical meson fields [37]. The Skyrme theory turned out to be remarkably successful in describing baryons in the previous decades [38]. Thus matter is supposed to arise from a pure geometric foundation [39,40]. Solitons are usually considered in the context of gauge transformations, which relate in a mathematical context to fiber bundles and Cartan geometries [22].With regards to the topics discussed above research in two-dimensional conformal field theories [41,42,43,44,45] has turned out to be important, also because conceptual insights can be obtained more easily in a lower dimensional geometry. Motivation to proceed in this direction is also provided by [31]. In this article the two-dimensional Euclidean plane and the conformal symmetries, which refer to the Laplace equation in R 2 , are fundamental in a sequence of higher dimensional geometries and Clifford algebras. Therefore, one can ask the question how the Laplace equation can be embedded into higher dimensional geometries. Here concepts like the stereographic projection should play an important role. In this sense one can consider the Laplace equation in the base space S 2 instead of R 2 by means of what is denoted here as holographic coordinates. This conceptual change is adopt...

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Higher spin currents in orthogonal Wolf space

Cited by 21 publications

References 105 publications

The operator product expansion between the 16 lowest higher spin currents in the $$\mathcal{N}=4$$ N = 4 superspace

The operator product expansion between the 16 lowest higher spin currents in the $$\mathcal{N}=4$$ N = 4 superspace

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

Holographic coordinates

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