No N=4 Strings on Wolf Spaces

TL;DR

This paper extends the N=2 supersymmetric coset construction to N=4, explores geometric constraints leading to Wolf spaces, and finds that these spaces cannot serve as consistent string backgrounds due to BRST charge conditions.

Contribution

It introduces a generalized N=4 coset construction with simple geometric interpretation and demonstrates the incompatibility of Wolf spaces as string backgrounds.

Findings

Wolf spaces are natural solutions to the geometric constraints.

The constructed N=4 models align with known supersymmetric sigma-models.

BRST nilpotency rules out Wolf spaces as string backgrounds.

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.