No N=4 Strings on Wolf Spaces

Abstract

We generalize the standard $N=2$ supersymmetric Kazama-Suzuki coset construction to the $N=4$ case by requiring the {\it non-linear} (Goddard-Schwimmer) $N=4$ quasi-superconformal algebra to be realized on cosets. The constraints that we find allow very simple geometrical interpretation and have the Wolf spaces as their natural solutions. Our results obtained by using components-level superconformal field theory methods are fully consistent with standard results about $N=4$ supersymmetric two-dimensional non-linear sigma-models and $N=4$ WZNW models on Wolf spaces. We construct the actions for the latter and express the quaternionic structure, appearing in the $N=4$ coset solution, in terms of the symplectic structure associated with the underlying Freudenthal triple system. Next, we gauge the $N=4$ QSCA and build a quantum BRST charge for the $N=4$ string propagating on a Wolf space. Surprisingly, the BRST charge nilpotency conditions rule out the non-trivial Wolf spaces as consistent string backgrounds.

31 pages, LaTeX, special macros are included

References in corpus (5)

• Ultra-Multiplets: A New Representation of Rigid 2D, N = 8 Supersymmetry
• Massive sigma models with (p,q) supersymmetry
• N=4 Superconformal Algebras and Gauged WZW Models
• The BRST Operator for the Large $N=4$ Superconformal Algebra
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Cited by in corpus (13)

• Large N=4 Holography
• Seven-Sphere and the Exceptional N=7 and N=8 Superconformal Algebras
• Higher Spin Currents in Wolf Space: Part I
• Higher Spin Currents in Orthogonal Wolf Space
• The $\mathcal{N}=4$ Coset Model and the Higher Spin Algebra
• The Next $16$ Higher Spin Currents and Three-Point Functions in the Large $\mathcal{N}=4$ Holography
• A Realization of N=1 $\mathcal{S}\mathcal{W}(3/2,2)$ Algebras with Wolf Spaces
• Three Point Functions in the N=4 Orthogonal Coset Theory
• The Operator Product Expansions in the $\mathcal{N}=4$ Orthogonal Wolf Space Coset Model
• Adding Complex Fermions to the Grassmannian-like Coset Model
• Exact renormalization flow and domain walls from holography
• Higher Spin Currents with Manifest $SO(4)$ Symmetry in the Large $\mathcal{N}=4$ Holography
• Wolf Space Coset Spectrum in the Large $\mathcal{N}=4$ Holography