1997/02/07 by C.M. Hull, C. M. Hull · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Quantum Chromodynamics and Particle Interactions #hep-th
paper · pdf · doi:10.1016/s0550-3213(97)00492-6
published as Nucl.Phys. B509 (1998) 252-272 · 32 pages, phyzzx macro
arxiv created 1997/02/07 · openalex publication_date 1998/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Effective actions are derived for (2,0) and (2,1) superstrings by studying the corresponding sigma-models. The geometry is a generalisation of Kahler 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 hyperkahler 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. Kahler and related geometries are generalised to ones involving real structures.