Local heterotic geometry in holomorphic coordinates

Details Local heterotic geometry in holomorphic coordinates Local heterotic geometry in holomorphic coordinates

1994-01-03

arxiv.org/abs/hep-th/9401003v2

Class.Quant.Grav.11:1133-1154,1994

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, latex file, report number PAR/LPTHE/93-56

Scientific paper

10.1088/0264-9381/11/5/004

In the same spirit as done for N=2 and N=4 supersymmetric non-linear $\si$ models in 2 space-time dimensions by Zumino and Alvarez- Gaum\'e and Freedman, we analyse the (2,0) and (4,0) heterotic geometry in holomorphic coordinates. We study the properties of the torsion tensor and give the conditions under which (2,0) geometry is conformally equivalent to a (2,2) one. Using additional isometries, we show that it is difficult to equip a manifold with a closed torsion tensor, but for the real 4 dimensional case where we exhibit new examples. We show that, contrarily to Callan, Harvey and Strominger 's claim for real 4 dimensional manifolds, (4,0) heterotic geometry is not necessarily conformally equivalent to a (4,4) K\"ahler Ricci flat geometry. We rather prove that, whatever the real dimension be, they are special quasi Ricci flat spaces, and we exemplify our results on Eguchi-Hanson and Taub-NUT metrics with torsion.

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