Normal Coordinates in Kahler Manifolds and the Background Field Method

Details Normal Coordinates in Kahler Manifolds and the Background Field Method Normal Coordinates in Kahler Manifolds and the Background Field Method

2002-03-08

arxiv.org/abs/hep-th/0203081v3

Prog.Theor.Phys. 108 (2002) 185-202

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX2e, 24 pages, no figures, the version to appear in Prog. Theor. Phys. 108

Scientific paper

10.1143/PTP.108.185

Riemann normal coordinates (RNC) are unsuitable for \kahler manifolds since they are not holomorphic. Instead, \kahler normal coordinates (KNC) can be defined as holomorphic coordinates. We prove that KNC transform as a holomorphic tangent vector under holomorphic coordinate transformations, and therefore that they are natural extensions of RNC to the case of \kahler manifolds. The KNC expansion provides a manifestly covariant background field method preserving the complex structure in supersymmetric nonlinear sigma models.

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