Actions for (2, 1) sigma models and strings

doi:10.1016/S0550-3213(97)00492-6

Nuclear Physics B

Volume 509, Issues 1–2, 5 January 1998, Pages 252-272

https://doi.org/10.1016/S0550-3213(97)00492-6 Get rights and content

Abstract

Effective actions are derived for (2, 0) and (2, 1) superstrings by studying the corresponding sigma models. The geometry is a generalisation of Ka¨hler geometry involving torsion and the field equations imply that the curvature with torsion is self-dual in four dimensions, or has SU(n,m) holonomy in other dimensions. The Yang-Mills fields are self-dual in four dimensions and satisfy a form of the Uhlenbeck-Yau equation in higher dimensions. In four dimensions with Euclidean signature, there is a hyperKa¨hler structure and the sigma model has (4, 1) supersymmetry, while for signature (2, 2) there is a hypersymplectic structure consisting of a complex structure squaring to -1 and two “real structures” squaring to 1. The theory is invariant under a twisted form of the (4, 1) superconformal algebra which includes an SL (2,R) Kac-Moody algebra instead of an SU(2) Kac-Moody algebra. Ka¨hler and related geometries are generalised to ones involving real structures.

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Actions for (2, 1) sigma models and strings

Abstract

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