Normal Coordinates in Kahler Manifolds and the Background Field Method
Kiyoshi Higashijima, Etsuko Itou, Muneto Nitta
Abstract
Riemann normal coordinates (RNC) are unsuitable for manifolds since they are not holomorphic. Instead, 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 manifolds. The KNC expansion provides a manifestly covariant background field method preserving the complex structure in supersymmetric nonlinear sigma models.
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