No N=4 Strings on Wolf Spaces

Details No N=4 Strings on Wolf Spaces No N=4 Strings on Wolf Spaces

1995-01-31

arxiv.org/abs/hep-th/9501140v1

Phys.Rev. D52 (1995) 2278-2293

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, LaTeX, special macros are included

Scientific paper

10.1103/PhysRevD.52.2278

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.

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