Wolf Space Coset Spectrum in the Large $\mathcal{N}=4$ Holography

Abstract

After reviewing the four eigenvalues (the conformal dimension, two $SU(2)$ quantum number, and $U(1)$ charge) in the minimal (and higher) representations in the Wolf space coset where the $\mathcal{N}=4$ superconformal algebra is realized by $11$ currents in nonlinear way, these four eigenvalues in the higher representations up to three boxes (of Young tableaux) are examined in detail. The eigenvalues associated with the higher spin-$1,2,3$ currents in the (minimal and) higher representations up to two boxes are studied. They are expressed in terms of the two finite parameters $(N,k)$ where the Wolf space coset contains the group $SU(N+2)$ and the affine Kac-Moody spin $1$ current has the level $k$. Under the large $(N,k)$ 't Hooft-like limit, they are simply linear combinations of the eigenvalues in the minimal representations. For the linear case where the $\mathcal{N}=4$ superconformal algebra is realized by $16$ currents in linear way, the eigenvalues, corresponding to the spin $2$ current and the higher spin $3$ current, which are the only different quantities (compared to the nonlinear case), are also obtained at finite $(N,k)$. They coincide with the results for the nonlinear case above after the large $(N,k)$ 't Hooft-like limit is taken. As a by product, the three-point functions of the higher spin currents with two scalar operators can be determined at finite $(N,k)$.

155 pages

References in corpus (8)

• Symmetries of Holographic Minimal Models
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• Two-dimensional $\mathcal{N}=(2,2)$ Lattice Gauge Theories with Matter in Higher Representations
• Three point functions in higher spin AdS_3 holography with 1/N corrections

Cited by in corpus (3)

• 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