Normal coordinates in Kähler manifolds and the background field method

Kiyoshi Higashijima, Etsuko Itou, Muneto Nitta

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27 Citations (Scopus)

Abstract

Riemann normal coordinates (RNC) are unsuitable for Kähler manifolds since they are not holomorphic. Instead, Kähler 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 Kähler manifolds. The KNC expansion provides a manifestly covariant background field method preserving the complex structure in supersymmetric nonlinear sigma models.

Original languageEnglish
Pages (from-to)185-202
Number of pages18
JournalProgress of Theoretical Physics
Volume108
Issue number1
DOIs
Publication statusPublished - 2002 Jul 1

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ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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