Adding Complex Fermions to the Grassmannian-like Coset Model

Abstract

In the $\mathcal{N}=2$ supersymmetric coset model, $\frac{SU(N+M{)}_k\times SO(2NM{)}_1}{SU(N{)}_{k+M}\times U(1{)}_{NM(N+M)(k+N+M)}}$, we construct the $SU(M)$ nonsinglet $\mathcal{N}=2$ multiplet of spins $(1,\frac{3}{2},\frac{3}{2},2)$ in terms of coset fields. The next $SU(M)$ singlet and nonsinglet $\mathcal{N}=2$ multiplets of spins $(2,\frac{5}{2},\frac{5}{2},3)$ are determined by applying the $\mathcal{N}=2$ supersymmetry currents of spin $\frac{3}{2}$ to the bosonic singlet and nonsinglet currents of spin $3$ in the bosonic coset model. We also obtain the operator product expansions(OPEs) between the currents of the $\mathcal{N}=2$ superconformal algebra and above three kinds of $\mathcal{N}=2$ multiplets. These currents in two dimensions play the role of the asymptotic symmetry, as the generators of $\mathcal{N}=2$ "rectangular $W$-algebra", of the $M\times M$ matrix generalization of $\mathcal{N}=2$ $Ad{S}_3$ higher spin theory in the bulk. The structure constants in the right hand sides of these OPEs are dependent on the three parameters $k,N$ and $M$ explicitly. Moreover, the OPEs between $SU(M)$ nonsinglet $\mathcal{N}=2$ multiplet of spins $(1,\frac{3}{2},\frac{3}{2},2)$ and itself are analyzed in detail. The complete OPE between the lowest component of the $SU(M)$ singlet $\mathcal{N}=2$ multiplet of spins $(2,\frac{5}{2},\frac{5}{2},3)$ and itself is described. In particular, when $M=2$, it is known that the above $\mathcal{N}=2$ supersymmetric coset model provides the realization of the extension of the large $\mathcal{N}=4$ nonlinear superconformal algebra. We determine the currents of the large $\mathcal{N}=4$ nonlinear superconformal algebra and the higher spin-$\frac{3}{2},2$ currents of the lowest $\mathcal{N}=4$ multiplet for generic $k$ and $N$ in terms of the coset fields.

85 pages

References in corpus (14)

• Higher Spins & Strings
• Higher spin AdS_3 holography with extended supersymmetry
• The symmetry of large N=4 holography
• The Worldsheet Dual of Free Super Yang-Mills in 4D
• Strange Metals in One Spatial Dimension
• The Continuous Orbifold of N=2 Minimal Model Holography
• Higher Spin Currents in Wolf Space: Part II
• Higher Spin Currents in Orthogonal Wolf Space
• Higher Spin Currents in Wolf Space for Generic N
• Higher Spin Currents in the Enhanced N=3 Kazama-Suzuki Model
• A Supersymmetric Enhancement of $\mathcal{N}=1$ Holographic Minimal Model
• The Operator Product Expansions in the $\mathcal{N}=4$ Orthogonal Wolf Space Coset Model
• The matrix-extended $W_{1+\infty }$ algebra
• Fermionic Construction in the Supersymmetric Coset Model

Cited by in corpus (1)

• Toward A Supersymmetric $w_{1+\infty }$ Symmetry in the Celestial Conformal Field Theory