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

Ahn, Changhyun; Kim, Man Hea

doi:10.1007/jhep02(2021)123

“…In the context of AdS 3 /CF T 2 correspondence, the previous algebra in (2.1) is related to the case of vanishing 't Hooft-like coupling constant. Therefore, it is an open question how the another deformed case with nonvanishing 't Hooft-like coupling constant [56] will arise in the context of the present paper. We expect that the currents from the free field realization will depend on this nonzero coupling constant explicitly and they will become the currents we have described in this paper by taking this coupling constant to be zero.…”

Section: Discussionmentioning

confidence: 95%

A Deformed Supersymmetric $w_{1+\infty}$ Symmetry in the Celestial Conformal Field Theory

Ahn¹

2022

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By using the K-free complex bosons and the K-free complex fermions, we construct the N = 2 supersymmetric W K,K ∞ algebra which is the matrix generalization of previous N = 2 supersymmetric W ∞ algebra. By twisting this N = 2 supersymmetric W K,K ∞ algebra, we obtain the N = 1 supersymmetric W K ∞ algebra which is the matrix generalization of known N = 1 supersymmetric topological W ∞ algebra. From this two-dimensional symmetry algebra, we propose the operator product expansion (OPE) between the soft graviton and gravitino (as a first example), at nonzero deformation parameter, in the supersymmetric Einstein-Yang-Mills theory explicitly. Other six OPEs between the graviton, gravitino, gluon and gluino can be determined completely. At vanishing deformation parameter, we reproduce the known result of Fotopoulos, Stieberger, Taylor and Zhu on the above OPEs via celestial holography.

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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%

“…According to the result of [3] on the holography, it is natural to ask whether we can construct the corresponding N = 2 higher spin algebra in the supersymmetric coset model in this paper. For M = 2, there is a construction in [71]. For generic M, it is an interesting problem to obtain them explicitly.…”

Section: Discussionmentioning

confidence: 99%

Adding Complex Fermions to the Grassmannian-like Coset Model

Ahn

2021

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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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“…In doing this, the new quasi primary spin-5 current will be determined. In the bulk theory side, it is an open problem to construct an extension of the higher spin algebra studied in [33,34] relevant works are given in [24,32,[36][37][38] and we will keep track of the nonsinglet parts of the construction. The nontrivial part is to identify the SU(M ) adjoint indices in the three point functions explicitly.…”

Section: Discussionmentioning

confidence: 99%

The Grassmannian-like coset model and the higher spin currents

Ahn

¹

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.

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

Cited by 15 publications

References 62 publications

A Deformed Supersymmetric $w_{1+\infty}$ Symmetry in the Celestial Conformal Field Theory

A Deformed Supersymmetric $w_{1+\infty}$ Symmetry in the Celestial Conformal Field Theory

Adding Complex Fermions to the Grassmannian-like Coset Model

The Grassmannian-like coset model and the higher spin currents

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