Higher Spin Currents in the Holographic N=1 Coset Minimal Model

Abstract

In the N=1 supersymmetric coset minimal model based on (B_N^{(1)} \oplus D_N^{(1)}, D_N^{(1)}) at level (k,1) studied recently, the standard N=1 super stress tensor of spins (3/2,2) is reviewed. By considering the stress tensor in the coset (B_N^{(1)}, D_N^{(1)}) at level k, the higher spin-2' Casimir current was obtained previously. By acting the above spin-3/2 current on the higher spin-2' Casimir current, its superpartner, the higher spin-5/2 current, can be generated and combined as the first higher spin supercurrent with spins (2', 5/2). By calculating the operator product expansions (OPE) between the higher spin supercurrent and itself, the next higher spin supercurrent can be generated with spins (7/2,4). Moreover, the other higher spin supercurrent with spins (4',9/2) can be generated by calculating the OPE between the first higher spin supercurrent with spins (2', 5/2) and the second higher spin supercurrent with spins (7/2,4). Finally, the higher spin supercurrent, (11/2,6), can be extracted from the right hand side of OPE between the higher spin supercurrents, (2', 5/2) and (4', 9/2).

97 pages; footnotes 1, 7 and 9 and the last paragraph of Appendix F added and to appear in JHEP

References in corpus (7)

• Large N=4 Holography
• Extended higher spin holography and Grassmannian models
• Even spin minimal model holography
• Higher Spin Currents with Arbitrary N in the N=1 Stringy Coset Minimal Model
• The $\mathcal{N}=1$ algebra ${\mathcal{W}}_{\infty }[\mu ]$ and its truncations
• Higher Spin Currents in the N=2 Stringy Coset Minimal Model
• Spin-5 Casimir Operator and Its Three-Point Functions with Two Scalars

Cited by in corpus (14)

• On the coset duals of extended higher spin theories
• 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
• 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
• 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
• The Operator Product Expansions in the $\mathcal{N}=4$ Orthogonal Wolf Space Coset Model
• Higher Spin Currents with Manifest $SO(4)$ Symmetry in the Large $\mathcal{N}=4$ Holography