Higher spin currents in the holographic $ \mathcal{N} $ = 1 coset minimal model

Abstract

In the N = 1 supersymmetric coset minimal model based on (B (1) N ) 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 ).

Three point functions in the large N = 4 $$ \mathcal{N}=4 $$ holography

“…The zero mode eigenvalue equations depend on N and k. It would be interesting to study the representation theory concerning on the higher spin currents further by generalizing the previous works in [6]. Under the large N 't Hooft limit, the nonzero eigenvalue corresponding to the quadratic higher spin-2 currents V , 33 For the light state, one obtains (1)+i 1Ṽ…”

Three-point functions in the 𝒩 = 4 orthogonal coset theory

“…The minimal representations are given by two representations. See also the previous works in [15,16,17,18,19]. One minimal representation is given by (0; v), where the nonnegative integer mode of the spin-1 current V a (z) inŝo(N + 4) acting on the state |(0; v) > vanishes.…”

The next 16 higher spin currents and three-point functions in the large $$\mathcal{N}=4$$ N = 4 holography

“…It is straightforward to apply the work of [6] and the presentation of this paper to the orthogonal case [54] in the context of [55][56][57][58][59]. The lowest 16 higher spin currents contains the higher spin 2 current as its lowest component.…”