The Geometry of $N=2$ Strings with Torsion

Abstract

$N=2$ 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.

10 pages, phyzzx, no figures. The discussion of conformal invariance is improved, and the class of geometries considered is generalised to include general dilaton backgrounds, in which the dilaton is the Killing potential for a holomorphic isometry

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• Off-Shell Formulation of N=2 Non-Linear Sigma-Models
• Actions For (2,1) Sigma-Models and Strings
• The Quantum Geometry of N=(2,2) Non-Linear Sigma-Models
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• The Geometry of Sigma-Models with Twisted Supersymmetry
• Einstein Supergravity and New Twistor String Theories
• Noncommutative Solitons and Quasideterminants
• Compact complex surfaces with geometric structures related to split quaternions
• D-branes in N=2 Strings
• Families of N=2 Strings
• The Effective Action and Geometry of Closed N=2 Strings
• Notes on S-Matrix of Non-critical N=2 String
• N=2 Strings on Orbifolds
• Effective Equations on the 3-Brane World from Type IIB String