The Geometry of $N=2$ Strings with Torsion

Details The Geometry of $N=2$ Strings with Torsion The Geometry of $N=2$ Strings with Torsion

1996-06-28

arxiv.org/abs/hep-th/9606190v3

Phys.Lett. B387 (1996) 497-501

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, phyzzx, no figures. The discussion of conformal invariance is improved, and the class of geometries considered is ge

Scientific paper

10.1016/0370-2693(96)01055-6

$N=2$ string theories are formulated in space-times with 2 space and 2 time dimensions. If the world-sheet matter system consists of 2 chiral superfields, the space-time is Kahler and the dynamics are those of anti-self-dual gravity. If instead one chiral superfield and one twisted chiral superfield are used, the space-time is a hermitian manifold with torsion and a dilaton. The string spectrum consists of a scalar, which is a potential $K$ determining the metric, torsion and dilaton. The dynamics imply that the curvature with torsion is anti-self-dual, and an action is found for the potential $K$. It is argued that any $N=2$ sigma-model with twisted chiral multiplets in any dimension can be deformed to a conformally invariant theory if the lowest order contribution to the conformal anomaly vanishes. If there are isometries, more general geometries are possible in which the dilaton is the Killing potential for a holomorphic Killing vector.

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