## 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)}⊕ 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}).

Original language | English |
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Article number | 12 |

Journal | Journal of High Energy Physics |

Volume | 2014 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2014 |

## Keywords

- AdS-CFT Correspondence
- Conformal and W Symmetry