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.

arXiv comment85 pages

References in corpus (67)

• W-symmetry in Conformal Field Theory
• An AdS_3 Dual for Minimal Model CFTs
• Higher-Spin Gauge Interactions for Massive Matter Fields in 3D AdS Space-Time
• Minimal Model Holography
• Black holes in three dimensional higher spin gravity: A review
• Triality in Minimal Model Holography
• Higher Spins & Strings
• Large N=4 Holography
• Higher spin AdS_3 supergravity and its dual CFT
• A holographic dual for string theory on ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$
• The Large N 't Hooft Limit of Coset Minimal Models
• Super-W(infinity) Asymptotic Symmetry of Higher-Spin AdS(3) Supergravity
• String Theory as a Higher Spin Theory
• Duality in N=2 minimal model holography
• Extended higher spin holography and Grassmannian models
• Higher spin AdS_3 holography with extended supersymmetry
• Strings on ${\text{AdS}}_3\times {\text{S}}^3\times {\text{S}}^3\times {\text{S}}^1$
• The Coset Spin-4 Casimir Operator and Its Three-Point Functions with Scalars
• Supersymmetric holography on AdS3
• The symmetry of large N=4 holography
• The Worldsheet Dual of Free Super Yang-Mills in 4D
• Strange Metals in One Spatial Dimension
• 3D Higher-Spin Gauge Theories with Matter
• Three point functions in higher spin AdS_3 supergravity
• The Large N 't Hooft Limit of Kazama-Suzuki Model
• Symmetries of Holographic Super-Minimal Models
• Explicit generators in rectangular affine W-algebras of type A
• Stringy $\mathcal{N}=(2,2)$ holography for AdS${}_3$
• Higher Spin Currents in Wolf Space: Part I
• The Primary Spin-4 Casimir Operators in the Holographic SO(N) Coset Minimal Models
• Rectangular W-algebras, extended higher spin gravity and dual coset CFTs
• Higher Spin Currents in the N=1 Stringy Coset Minimal Model
• Higher spin algebras and large $\mathcal{N}=4$ holography
• Rectangular W-(super)algebras and their representations
• 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
• The Continuous Orbifold of N=2 Minimal Model Holography
• 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
• Spin-5 Casimir Operator and Its Three-Point Functions with Two Scalars
• No N=4 Strings on Wolf Spaces
• Higher Spin Currents in the Holographic N=1 Coset Minimal Model
• The large $\mathcal{N}=4$ superconformal ${\mathcal{W}}_{\infty }$ algebra
• The OPEs of Spin-4 Casimir Currents in the Holographic SO(N) Coset Minimal Models
• Higher Spin Currents in Wolf Space: Part II
• Higher Spin Currents in Orthogonal Wolf Space
• Geometric interpretation of the large N=4 index
• Higher Spin Currents in Wolf Space for Generic N
• Rectangular W-algebras of types $so(M)$ and $sp(2M)$ and dual coset CFTs
• Higher Spin Currents in Wolf Space: Part III
• The Next $16$ Higher Spin Currents and Three-Point Functions in the Large $\mathcal{N}=4$ Holography
• Higher Spin Currents in the Enhanced N=3 Kazama-Suzuki Model
• The symmetric orbifold of N=2 minimal models
• The $\mathcal{N}=4$ Coset Model and the Higher Spin Algebra
• The $\mathcal{N}=4$ Higher Spin Algebra for Generic $\mu$ Parameter
• Three Point Functions in the N=4 Orthogonal Coset Theory
• Even spin $\mathcal{N}=4$ holography
• Higher Spin Currents in the Orthogonal Coset Theory
• A Supersymmetric Enhancement of $\mathcal{N}=1$ Holographic Minimal Model
• The Operator Product Expansions in the $\mathcal{N}=4$ Orthogonal Wolf Space Coset Model
• A note on the $\mathcal{N}=2$ super-${\mathcal{W}}_3$ holographic dictionary
• Wolf Space Coset Spectrum in the Large $\mathcal{N}=4$ Holography
• The Grassmannian-like Coset Model and the Higher Spin Currents
• Higher Spin Currents with Manifest $SO(4)$ Symmetry in the Large $\mathcal{N}=4$ Holography
• The Grassmannian VOA
• The matrix-extended $W_{1+\infty }$ algebra
• Fermionic Construction in the Supersymmetric Coset Model

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