Normal coordinates in Kähler manifolds and the background field method

Kiyoshi Higashijima, Etsuko Itou, Muneto Nitta

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2002 Jul
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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