Spin-5 Casimir Operator and Its Three-Point Functions with Two Scalars

Abstract

By calculating the second-order pole in the operator product expansion (OPE) between the spin-3 Casimir operator and the spin-4 Casimir operator known previously, the spin-5 Casimir operator is obtained in the coset model based on (A_{N-1}^{(1)} \oplus A_{N-1}^{(1)}, A_{N-1}^{(1)}) at level (k,1). This spin-5 Casimir operator consisted of the quintic, quartic (with one derivative) and cubic (with two derivatives) WZW currents contracted with SU(N) invariant tensors. The three-point functions with two scalars for all values of 't Hooft coupling in the large N limit were obtained by analyzing the zero-mode eigenvalue equations carefully. These three-point functions were dual to those in AdS_3 higher spin gravity theory with matter. Furthermore, the exact three-point functions that hold for any finite N and k are obtained. The zero mode eigenvalue equations for the spin-5 current in CFT coincided with those of the spin-5 field in asymptotic symmetry algebra of the higher spin theory on the AdS_3. This paper also describes the structure constant appearing in the spin-4 Casimir operator from the OPE between the spin-3 Casimir operator and itself for N=4, 5 in the more general coset minimal model with two arbitrary levels (k_1, k_2).

71 pages; many improvements in the whole paper done and to appear in JHEP

References in corpus (4)

• Symmetries of Holographic Minimal Models
• Large N=4 Holography
• Higher Spin Currents with Arbitrary N in the N=1 Stringy Coset Minimal Model
• Higher Spin Currents in the N=2 Stringy Coset Minimal Model

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• Higher Spin Currents in Wolf Space: Part I
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• The Operator Product Expansion between the 16 Lowest Higher Spin Currents in the N=4 Superspace
• Higher Spin Currents in the Holographic N=1 Coset Minimal Model
• Higher Spin Currents in Wolf Space for Generic N
• Higher Spin Currents in Orthogonal Wolf Space
• Higher Spin Currents in the Enhanced N=3 Kazama-Suzuki Model
• The Next $16$ Higher Spin Currents and Three-Point Functions in the Large $\mathcal{N}=4$ Holography
• Three point functions in higher spin AdS_3 holography with 1/N corrections
• Three Point Functions in the N=4 Orthogonal Coset Theory
• Higher Spin Currents in the Orthogonal Coset Theory
• Symmetry Algebras of Stringy Cosets
• Adding Complex Fermions to the Grassmannian-like Coset Model
• Higher Spin Currents with Manifest $SO(4)$ Symmetry in the Large $\mathcal{N}=4$ Holography