Higher Spin Currents with Arbitrary N in the N=1 Stringy Coset Minimal Model

Abstract

In the N=1 supersymmetric coset model based on (A_{N-1}^{(1)} \oplus A_{N-1}^{(1)}, A_{N-1}^{(1)}) at level (k, N), the lowest N=1 higher spin supercurrent with spins-(5/2, 3), in terms of two independent numerator WZW currents, is reviewed. By calculating the operator product expansions (OPE) between this N=1 higher spin supercurrent and itself, the next two N=1 higher spin supercurrents can be generated with spins-(7/2, 4) and (4, 9/2). These four currents are polynomials of degree 3, 4, 4, 4 in the first numerator WZW currents with level k. The complete nonlinear OPE of the lowest N=1 higher spin supercurrent for general N is obtained. The three-point functions involving two scalar primaries with one spin-2 current or spin-3 current are calculated in the large N limit for all values of the 't Hooft coupling. In particular, the light states that appeared in the case when the second level was fixed by 1 are no longer light ones because the eigenvalues are finite in the large N limit.

56 pages

References in corpus (7)

• Symmetries of Holographic Minimal Models
• Large N=4 Holography
• Even spin minimal model holography
• Strange Metals in One Spatial Dimension
• N=1 extension of minimal model holography
• The $\mathcal{N}=1$ algebra ${\mathcal{W}}_{\infty }[\mu ]$ and its truncations
• Higher Spin Currents in the N=2 Stringy Coset Minimal Model

Cited by in corpus (20)

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• Extended higher spin holography and Grassmannian models
• Higher spin AdS_3 holography with extended supersymmetry
• Higher Spin Currents in Wolf Space: Part I
• Higher Spin Currents in the N=2 Stringy Coset Minimal Model
• The Operator Product Expansion between the 16 Lowest Higher Spin Currents in the N=4 Superspace
• Spin-5 Casimir Operator and Its Three-Point Functions with Two Scalars
• Yangian associated with 2D $\mathcal{N}=1$ SCFT
• Higher Spin Currents in the Holographic N=1 Coset Minimal Model
• Higher Spin Currents in Wolf Space for Generic N
• The Next $16$ Higher Spin Currents and Three-Point Functions in the Large $\mathcal{N}=4$ Holography
• Higher Spin Currents in the Enhanced N=3 Kazama-Suzuki Model
• Three Point Functions in the N=4 Orthogonal Coset Theory
• Symmetry Algebras of Stringy Cosets
• Higher Spin Currents in the Orthogonal Coset Theory
• A Supersymmetric Enhancement of $\mathcal{N}=1$ Holographic Minimal Model
• Adding Complex Fermions to the Grassmannian-like Coset Model
• Higher Spin Currents with Manifest $SO(4)$ Symmetry in the Large $\mathcal{N}=4$ Holography
• The Grassmannian-like Coset Model and the Higher Spin Currents
• Fermionic Construction in the Supersymmetric Coset Model