The Primary Spin-4 Casimir Operators in the Holographic SO(N) Coset Minimal Models

Abstract

Starting from SO(N) current algebra, we construct two lowest primary higher spin-4 Casimir operators which are quartic in spin-1 fields. For N is odd, one of them corresponds to the current in the WB_{\frac{N-1}{2}} minimal model. For N is even, the other corresponds to the current in the WD_{\frac{N}{2}} minimal model. These primary higher spin currents, the generators of wedge subalgebra, are obtained from the operator product expansion of fermionic (or bosonic) primary spin-N/2 field with itself in each minimal model respectively. We obtain, indirectly, the three-point functions with two real scalars, in the large N 't Hooft limit, for all values of the 't Hooft coupling which should be dual to the three-point functions in the higher spin AdS_3 gravity with matter.

65 pages; present the main results only and to appear in JHEP where one can see the Appendix

References in corpus (7)

• Symmetries of Holographic Minimal Models
• Higher spin AdS_3 supergravity and its dual CFT
• Partition functions of higher spin black holes and their CFT duals
• Correlation Functions in Holographic Minimal Models
• Towards non-AdS holography in 3-dimensional higher spin gravity
• The Coset Spin-4 Casimir Operator and Its Three-Point Functions with Scalars
• Limits of minimal models and continuous orbifolds

Cited by in corpus (21)

• N=1 supersymmetric higher spin holography on AdS_3
• Even spin minimal model holography
• Three point functions in higher spin AdS_3 supergravity
• The Large N 't Hooft Limit of Kazama-Suzuki Model
• Higher Spin Currents in Wolf Space: Part I
• Higher Spin Currents in the N=1 Stringy Coset Minimal Model
• Higher Spin Currents with Arbitrary N in the N=1 Stringy Coset Minimal Model
• The Operator Product Expansion of the Lowest Higher Spin Current at Finite N
• Higher Spin Currents in the N=2 Stringy Coset Minimal Model
• Spin-5 Casimir Operator and Its Three-Point Functions with Two Scalars
• 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 the N=4 Orthogonal Coset Theory
• Conformal embeddings and higher-spin bulk duals
• Higher Spin Currents in the Orthogonal Coset Theory
• The Operator Product Expansions in the $\mathcal{N}=4$ Orthogonal Wolf Space Coset 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